当前位置：文档库 › 专业英语翻译-main

专业英语翻译-main

Construction and Building Materials 18(2004)91–97

Modifying the mechanism method of masonry arch bridge analysis

K.-H.Ng,C.A.Fairfield*

School of the Built Environment,Napier University,10Colinton Road,Edinburgh EH105DT,UK Received 24April 2003;received in revised form 24April 2003;accepted 15August 2003

Abstract

A typical stone masonry arch bridge (Bargower bridge )was assessed by the mechanism method.The collapse load prediction from this method depended on the assumed distribution of lateral earth pressures on the extrados.The arch profile at the onset of failure deviated significantly from its original form.Mechanism analysis is accurate only when all the forces and their positions are known.The authors modified the mechanism method by including a deflection-dependent pressure updating algorithm.Results confirmed that arch deflections had a significant influence on the prediction of the assessed collapse load compared to that observed at Bargower.The problem of predicting exactly what deflection pertains to the collapse state remains a matter for future research.

Keywords:Brickwork and masonry;Bridges;Assessment methods

1.Introduction

The assessment of old arches is complicated by soil–structure interaction as discussed by Ng w 1x .An arch bridge’s capacity may also be assessed by the mecha-nism method as described in detail by Heyman w 2x .Collapse load predictions from this method depend on an assumed distribution of lateral soil pressures on the extrados regardless of the arch’s deformed shape.The arch profile at the onset of failure differs from its original shape.A mechanism analysis is accurate only when all the forces and their positions are known.A modified version of the mechanism method including geometrical non-linearity and a deflection-dependent backfill pressure distribution model is presented.Also investigated were the influence of:arch deflection,backfill ultimate active and passive deflections,live load dispersal angle,material densities and the backfill’s angle of shearing resistance on the predicted collapse load for Bargower bridge.This was a stone masonry arch tested to destruction by Hendry et al.w 3x in 1986on behalf of what is now the Transport Research Laboratory.This work does not purport to be yet another

*Corresponding author.Tel.:q 44-131-455-2232;fax:q 44-131-455-2239.

E-mail address:c.fairfield@https://www.wendangku.net/doc/349345396.html, (C.A.Fairfield ).

arch assessment method;like previous work by Ng and Fairfield elsewhere w 4x it is best viewed as complemen-tary to existing assessment methods.2.Method

An intact masonry arch is statically indeterminate.It becomes determinate when three hinges form in the arch ring under live load.In the mechanism method,the arch is assumed to be about to collapse under a single axle load on the pavement surface somewhere at approxi-mately one -span point.Four hinge positions are 1y 4selected to search for the minimum collapse load taking into account all forces acting whilst still fully containing the thrustline within the arch ring.

Fig.1shows an arch at collapse with four hinges (A–D ).As in the conventional mechanism method,there are three unknowns:the live load,the vertical abutment reaction and the horizontal abutment reaction each of which must be found to describe the thrustline.Taking moments about A,B and C,three equilibrium equations are derived.In the authors’modified method,the arch could not transmit tensile stress and was infinitely strong in compression.The arch was idealised as a two-dimensional plane strain structure thereby ignoring the spandrel,wing and parapet walls.The three

92K.-H.Ng,C.A.Fairfield /Construction and Building Materials 18(2004)

91–97

Fig.1.Failure mechanism;origin at point A.

Table 1

Values of the variables used to analyse Bargower

bridge Variable

Value Span 10360mm Rise

5180mm Ring thickness

558mm Backfill depth at the crown

1200mm Location of the centreline of load platen y -span point 1

3Width of load platen 750mm Backfill bulk unit weight 20kN m y 3Arch bulk unit weight

21kN m y 3Backfill angle of shearing resistance 358Live load dispersal angle

458Ultimate active lateral deflection 10mm Ultimate passive lateral deflection

100mm

Fig.2.Bi-linear backfill lateral pressure model.Fig.3.Collapse load vs.permitted deflection.

unknowns can be evaluated explicitly and since the thrustline represents a line of zero bending moment,its position can be determined by taking moments about any point within the span.Fig.2shows the bi-linear backfill pressure distribution model incorporated in the authors’modified mechanism method.This model is fully described by specifying the backfill’s angle of shearing resistance,its ultimate active deflection and its ultimate passive deflection.The backfill lateral pressure coefficient is evaluated using Rankine’s theory of lateral earth pressure.

This modified mechanism method has been coded in FORTRAN for general use.Bargower bridge (used here as a test case )has the geometrical and material proper-ties given in Table 1.In the ensuing study,each parameter was varied individually whilst keeping the rest unchanged with their baseline values.The program allowed the user to specify an arch vertical deflection at hinge B.This pre-set,user defined,value of deflection forces the arch to assume a shape unique to that deflected state.The mechanism is then evaluated in terms of the forces and deflections required to bring the arch to this state.Of these forces the key,and objective of this exercise,is the collapse load.3.Bargower bridge

Bargower bridge was built in 1859with a span of 10360mm,a 168skew angle,and a semicircular profile.

Its geometrical and material properties were given in Table 1.No major defects were observed before testing and its condition was described as ‘moderate’.At a depth of approximately 1m below the road surface,the fill was composed of large boulders interspersed with fine sand and silt.The fill above this level was a silty sand.The arch was tested to collapse under a line load of 750mm width located at one -span point.The 1y 3maximum recorded applied load was 645kN m width.y 1Collapse was due to combined compressive and mech-anism failures.4.Results

Results generated with the standard input variables (Table 1)are presented.These are followed by the results of a parametric study involving:the ultimate active and passive lateral deflections,backfill and arch unit weights,backfill angle of shearing resistance and live load dispersal angle.Unless otherwise stated the arch vertical deflection refers to that under the load platen’s centreline.

K.-H.Ng,C.A.Fairfield /Construction and Building Materials 18(2004)

91–97Fig.4.Predicted mechanism at 645kN m .

1Fig.5.Distribution of lateral pressure coefficient for various deflec-tions under the load

line.

Fig.6.The effect of ultimate active deflection.

4.1.Baseline case:analytical results

Fig.3shows the predicted arch collapse loads for different permitted arch vertical deflections.The pre-dicted arch collapse load was 645kN m expressed as y 1a line load normal to the span (i.e.matching that observed experimentally )but this was only the case for an arch vertical deflection of 32mm.The corresponding collapse mode is shown in Fig.4with the deformed geometry exaggerated for clarity.Fig.5shows the effect of arch deflection on the distribution of backfill lateral pressure coefficient.With no arch deflection,an at-rest pressure coefficient of 0.43was recorded everywhere around the extrados except at the crown where the coefficient was zero since the slope of the intact arch at the crown was zero.By applying arch deflections,both backfill active and passive resistances were mobilised to a degree dependent upon the arch deflection.One of the consequences of introducing arch deflections was to shift the point which was initially subjected to no lateral backfill pressure from the crown towards the side remote from the load.This was because the point where the extrados had zero slope had no longer remained at the crown under the applied deflection.With an arch vertical deflection of 14mm,the maximum passive pressure coefficient was found to be 1.65(corresponding to a mobilised f9value of 148)at a horizontal distance of 7190mm from the left abutment.This equated to 44%mobilisation of the permitted full passive resistance in terms of f9and only 37%with respect to the permissible ultimate passive deflection.For a similar arch vertical deflection,full mobilisation of active resistance was recorded at most points on the loaded side.This was because full mobilisation of active resistance required only 10mm lateral deflection in this analysis.By applying arch vertical deflections of 32,42,52and 62mm,the maximum evaluated passive coefficients were 3.04,3.69,3.69and 3.69,respectively.Although a zone of full mobilisation of passive resistance was recorded with an arch vertical deflection of 42mm and beyond,it covered only a limited area and its magnitude was

found to be gradually reduced to the at-rest coefficient of earth pressure at the right hand abutment.

Fig.5compares the backfill lateral pressure coeffi-cient’s distribution evaluated using the authors’bi-linear model (Fig.2)and that assumed in a conventional mechanism method.Both methods predicted significant-ly different lateral pressure distributions.The distribution of lateral pressure coefficient used in a conventional mechanism method is unrealistic since a constant mob-ilisation of backfill lateral resistance on each side of an arch is impossible as horizontal deflections vary around the arch.As mentioned in section 4.2,once the deflec-tion exceeded 30mm,the backfill’s full active resistance was mobilised.Only then did the mechanism method’s idealised active pressure distribution become relevant and applicable to the collapse load analysis.

4.2.The effect of varying the ultimate active deflection Fig.6shows the insignificant effect of varying the backfill’s ultimate active deflection on the collapse

94K.-H.Ng,C.A.Fairfield/Construction and Building Materials18(2004)

91–97

Fig.7.The effect of ultimate passive

deflection.Fig.9.The effect of arch unit

weight.

Fig.8.The effect of backfill unit

weight.Fig.10.The effect of backfill f9value. predictions.All predictions converged for deflections

over30mm.Thereafter,the backfill’s full active resis-

tance was mobilised and the distribution of resistance

around the extrados remained unchanged at its full active

value even after further deflection.

4.3.The effect of varying the ultimate passive deflection

Fig.7shows the effect of varying the ultimate passive

deflection on the collapse load prediction.The lower

the backfill ultimate passive deflection the greater its

influence on the capacity.For a backfill ultimate passive

deflection of140mm,its influence was insignificant

because a much larger lateral deflection was required to

mobilise full passive resistance.The peak collapse loads

with backfill ultimate passive deflections of25,50,75,

100and140mm were:995,847,743,651and566

kN m,respectively.Full passive resistance was mob-

ilised at a deflection of75mm with an arch vertical

deflection of32mm.

4.4.The effect of varying the backfill unit weight

Fig.8shows the effect of varying the backfill’s unit

weight on the collapse load prediction.The predicted

capacity increased with the backfill unit weight for any

given arch vertical deflection.By increasing the backfill

unit weight from18to21kN m,the predicted peak

arch collapse load increased from602to691kN m y1

for an arch vertical deflection of42mm.

4.5.The effect of varying the arch unit weight

Fig.9shows the effect of varying the arch unit weight

on the predicted collapse load.Increasing the arch unit

weight was shown to increase the predicted collapse

load for any given vertical deflection.By increasing the

arch unit weight from19to22kN m,the peak

predicted arch collapse load was found to increase from

655to665kN m.

K.-H.Ng,C.A.Fairfield /Construction and Building Materials 18(2004)

91–97Fig.11.The effect of live load dispersal angle.

4.6.The effect of varying the backfill’s angle of shearing resistance,f 9

Fig.10shows the effect of varying the backfill’s angle of shearing resistance,f9upon the predicted capacity.With the exception of very small arch vertical deflections,the capacity was higher with a higher backfill f9value.Setting f9s 258gave a predicted collapse load that reduced with increasing arch vertical deflections.For 35(f9(458the predicted arch collapse loads increased with arch vertical deflections until reach-ing their maxima at 661and 901kN m ,respectively.y 14.7.The effect of varying the live load dispersal angle Fig.11shows the effect of varying the live load dispersal angle on the collapse load prediction.Increas-ing load dispersal increased the assessed capacity over the range of deflections considered.Unlike the properties considered thus far,the live load dispersal angle was subjective and not directly measurable.Significant results arising from centrifuge tests on soil–arch systems are available from Cardiff’s research team led by Hughes et al.w 5x and supported by Burroughs et al.w 6x .5.Discussion

The following three sub-sections critically discuss:the key results arising from the application of the authors’proposed modifications to the mechanism meth-od of arch assessment,the effects that the imposition of certain necessary limiting assumptions may have had upon the assessed collapse capacity,and the limitations of the proposed extension to the mechanism method.5.1.Discussion:key results

The modified mechanism method predicted an arch collapse load of 645kN m with an arch vertical

y 1deflection of 32mm (equivalent to 45mm vertical movement at hinge C ).These results compared well with the test maximum applied load of 645kN m at y 1a vertical deflection of 32"0.5mm.Referring to Fig.3,it could be seen that the prediction of arch collapse load increased with arch deflection until it reached a maximum.The arch deflection had two major influences on the capacity prediction in this modified mechanism method.With a deflected arch,the thrustline migrates more readily to the intrados and extrados to form the failure mechanism thereby lowering the predicted col-lapse load.However,deflecting an arch simultaneously mobilises backfill resistance which stabilises the arch.The capacity of the deflected arch depended on the loss of strength due to the deflected arch geometry and the gain of strength due to mobilisation of passive resistance.In the case of Bargower bridge,the gain of strength due to mobilisation of passive resistance was found to be more significant than that lost due to the deflected geometry until a maximum vertical deflection of 42mm.Beyond this point the capacity was reduced.

Fig.5shows the influence of arch deflection on the backfill’s lateral pressure coefficient distribution.Full mobilisation of the passive resistance was found at an arch deflection of 42mm.The peak backfill passive coefficient did not occur at the crown since hinge C (Fig.1)was located away from the crown.A relatively small vertical deflection sufficed to fully mobilise the backfill’s active resistance.

The backfill ultimate active deflection did not have a significant influence upon the predicted collapse load and distribution of backfill pressure coefficient.This was because active forces were negligible compared to the system’s self-weight and the backfill’s passive resis-tance.It could be seen from Fig.6that at,and above,30mm vertical arch deflection,all capacity predictions were identical (regardless of the backfill’s chosen ulti-mate active deflection )because the active resistance was fully mobilised.

The backfill’s ultimate passive deflection had a dra-matic influence on the predicted arch collapse load and the distribution of the backfill lateral pressure coeffi-cient.It could be seen from Fig.7that,with lower backfill ultimate passive deflections,the predictions of arch collapse load were found to increase with arch deflections until they reached their maxima.Its influence was particularly significant in this case since Bargower bridge was a steep haunched arch with a significant amount of backfill on both sides of the span enhancing the soil–structure interaction effects.However,its influ-ence also depended on the backfill’s angle of shearing resistance.The effect would be more dramatic with a higher f9value.

The material unit weights influenced the capacity predictions.At Bargower bridge a substantial depth of fill of 1.2m was used to cover the arch rendering the

96K.-H.Ng,C.A.Fairfield/Construction and Building Materials18(2004)91–97

backfill unit weight so influential.However,the arch’s unit weight was found to have a comparatively low influence on the capacity assessment as its volume was lower than that of the backfill.

The live load dispersal angle had a significant influ-ence on the collapse load predictions.It is still a subject of dispute as to what actual live load dispersal angle should be used in this type of analysis.A278dispersal angle was suggested by the Department of Transport in 1997w7x.However,a live load dispersal angle of658 was recorded during full-scale testing of Kimbolton Butts bridge in1996by Ponniah et al.w8x.A458 dispersal angle was used in this research,except during the parametric study on the load dispersal angle itself.

5.2.Discussion:key assumptions

The authors’modified mechanism method assumes the arch has no tensile strength and infinite compressive strength.The former is justifiable since most arches have been cyclically loaded for over a century and therefore their residual tensile strength is negligible.The tensile strength of an arch would be more important only in the case of a newly built arch.

The compressive failure of the arch has been incor-porated in conventional mechanism assessments by Smith w9x.The arch’s compressive strength is a function of the combined compressive strength of the voussoir unit and the mortar joint.The combined compressive strength of a masonry prism is much lower than that of the voussoir itself since the failure of a masonry prism is due to a tensile stretching effect induced in the mortar which has a higher Poisson’s https://www.wendangku.net/doc/349345396.html,pressive failure of an arch happens,if at all,at hinges where the inter-voussoir contact area is markedly reduced.There are then stress concentrations due to the limited contact area between the voussoir and the mortar or,in the event of mortar loss over time,between voussoirs.This differs from the behaviour defined in the compressive failure of a masonry prism whose mechanics have been widely used by various researchers in the mechanism method. In reality,an apparent compressive failure occurs simul-taneously with the collapse of the arch.This implies that shortly before the occurrence of compressive failure the applied live load would have almost reached its maximum.One question remains:is reducing the arch ring thickness by considering a zone of thrust due to compressive failure a solution that adequately considers potential compressive failure in the mechanism method?

5.3.Discussion:method’s limitations

One of the difficulties in using the authors’modified mechanism method is determining the arch vertical deflection at which the applied load reaches its maxi-mum.This depends on the arch geometry as well as its material properties.Full-scale tests revealed that the arch vertical deflections by which the arch capacity had reached its maximum were between20and50mm. Research is underway to develop an empirical formula, using full-scale test results,to relate an arch’s vertical deflection with which it achieved its maximum capacity to its geometry.Apart from the aforementioned difficul-ties,the arch bridge is assumed to be idealised as a two-dimensional,plane strain structure in the mechanism method.This ignores contributions from the spandrel, wing and parapet walls.In reality,the arch behaviour and hinge positions change if the arch is not surrounded by these various walls.

6.Conclusions

A modified mechanism method has been successfully used to analyse Bargower bridge.A bi-linear backfill lateral pressure model was incorporated into a simple mechanism method making the backfill lateral pressure distribution more realistic.

Arch deflections affected the assessed capacity and the mobilised backfill lateral pressures.

The backfill’s ultimate passive deflection influenced the predicted collapse load but the corresponding active state deflections had little effect upon the assessed capacity.

The backfill and arch unit weights influenced the predicted collapse load:the former was more influential due to the backfill’s greater mass as a proportion of the self-weight.

The backfill’s angle of shearing resistance and its ability to disperse live load had a significant influence on the predicted collapse load.

References

w1x Ng K-H.Analysis of masonry arch bridges.Ph.D.thesis, Edinburgh:Napier University;1999.

w2x Heyman J.The masonry arch.Chichester:Ellis Horwood, 1982.

w3x Hendry A W,Davies SR,Royles R,Ponniah DA,Forde MC.

Load test to collapse on a masonry arch bridge at Bargower, Strathclyde.Contractor Report26,TRL,Crowthorne;1986.

w4x Ng K-H,Fairfield CA.Monte Carlo simulation for arch bridge assessment.Construct Build Mater2002;16(5):271–80.

w5x Hughes TG,Davies MCR,Taunton PR.Small scale modelling of brickwork arch bridges using a centrifuge.Proc Instn Civil Eng Struct Build1998;128:49–58.

w6x Burroughs PO,Baralos P,Hughes TG,Davies MCR.Service-ability load effects on masonry arch bridges.Proceedings of the Third International Conference of Arch Bridges.Paris;

2001.p.397–402.

97 K.-H.Ng,C.A.Fairfield/Construction and Building Materials18(2004)91–97

w7x Department of Transport.The assessment of highway bridges and structures.Departmental Standard BD21y97,HMSO,Lon-don;1997.

w8x Ponniah DA,Prentice DJ,Fairfield CA.The effect of the overlying fill on stresses in a new arch bridge.Proceedings of

the International Conference Recent Advances in Bridge Engng,CIMNE,Barcelona;1996.p.279–288.

w9x Smith FW.Load path analysis of masonry arches.Ph.D.thesis, Dundee:University of Dundee;1991.