J Shave, T Christie, S Denton, A Kidd
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DEVELOPMENT OF TRAFFIC SURCHARGE MODELS FOR HIGHWAY STRUCTURES J Shave, Parsons Brinckerhoff, Bristol, UK T Christie, Parsons Brinckerhoff, Bristol, UK S Denton, Parsons Brinckerhoff, Bristol, UK A Kidd, Highways Agency, Bedford, UK
Abstract Models have been developed to represent the horizontal load surcharges on abutment walls, wing walls and other earth retaining structures due to traffic loads. These models have been developed based based on an analysis of the global and local effects of the traffi c loads in the UK National Annex to BS EN1991-2, and are different from the uniform pressure approach of [1] BD37 . The recommended approach approach for abutments is based on the application of a horizontal uniform load together with knife-edged loads at the surface. For other structures such as wing walls a different is approach is needed, involving superposition of the effects of wheel loads. These [2] models have been incorporated into PD6694-1 for structures subject to traffic loading and designed to BS EN1997-1.
Notation All notation is based on the definitions of PD6694-1, BS EN 1991-2 and its National Annex.
Introduction
[2]
This paper describes the development of requirements as included in PD6694-1 for the modelling of horizontal surcharge effects caused by the vertical t raffic loading applied to the carriageway behind abutments, wing walls, side walls and other parts of the bridge in contact with earth. Before the introduction of Eurocodes, the standard approach for designing highway structures [1] for traffic surcharge effects in the UK followed the requirements of BD37/01 , which specified a vertical live load surcharge behind an abutment of 10kN/m² for HA loading and 20kN/m² for 45 units of HB loading (BD 37/01 5.8.2). This vertical load was typically converted into a horizontal earth pressure for design using an appropriate earth pressure [1] coefficient, K . The validity of the BD37/01 surcharge loads is somewhat questionable. The [3] 10kN/m² vertical surcharge for HA loading first appeared in BS153 , when it was approximately equivalent equivalent to the uniformly distributed load (UDL) component of HA loading over a 4.5m loaded length. However, the localised effects t hat would normally have been modelled with the knife edged edged load (KEL) component of HA loading were not included, and the magnitude of the surcharge loading was not updated to align with subsequent subsequent increases in allowable traffic weights.
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The 20kN/m² surcharge load that was intended to model 45 units of HB does not seem to be consistent with the magnitude of the HB load model (a single bogey for 45 units of HB had an average surface pressure of around 130kN/m², which is 6.5 times greater than the 20kN/m² surcharge load). [1]
The uniform pressure method of BD37/01 also does not realistically represent the distribution of pressures on the wall due to vehicle loading; the pressures should be more concentrated towards the top of the wall (this will be demonstrated later in the paper, based on a variety of analytical methods). With the implementation of Eurocodes it was necessary to develop rational models for surcharge based on the traffic loading specified in the UK National Annex to BS EN 1991-2 and satisfying the requirements of BS EN 1997-1. The new surcharge models as stated in PD6694-1 and described in t his paper were developed to properly account for surcharge effects, and are more realistic and also more onerous than the past practice as specified in BD37/01.
Traffic Load Models in BS EN 1991-2 The traffic loading for the carriageway behind abutments and wingwalls and other parts of structures in contact with the earth is covered by BS EN 1991-2, 4.9.1, and defined in the UK National Annex to BS EN 1991-2, NA.2.34. For normal traffic, the load model in Figure 1 is used in place of Load Model 1 (in this paper for convenience we refer to the load model in Figure 1 as the “equivalent LM1 vehicle”). The SV and SOV load models (as defined in UK National Annex to BS EN 1991-2, NA.2.16) may also be required. 65 kN
65 kN 1.2m
75 kN
115 kN 3.9m
1.3m
0.4m m 4 . 0
m 0 . 2
Figure 1. Load model for normal traffic (equivalent LM1 vehicle)
The axle loads in Figure 1 must be multiplied by an overload factor of 1.5 and a dynamic amplification factor (DAF) of 1.4, although for effects below the surface the National Annex allows the DAF for this vehicle and the SV and SOV vehicles to be r educed linearly to unity at a depth of 7m below the surface. (This slow rate of reduction is much more conservative [4] than allowed in the UK assessment standard BA55 and the Canadian Highway Bridge [5] Design Code CSA-S6 which both reduce the DAF to a minimum value at just 1.5m below the surface.) For vehicles in lanes other than lane 1, the loads should also be reduced by a lane factor as defined in BS EN 1991-2.
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If the vehicle weights (including the overload factor and the DAF) are assumed to be uniformly distributed over the plan area of the vehicle (or axle group) the resulting average vertical pressures at surface level are as given in Table 1. These are considerably higher than [1] the 10kN/m² for HA loading and 20kN/m² for HB loading specified in BD 37 . Average pressure under one equivalent LM1 vehicle Average pressure under rear pair of equivalent LM1 axles Average pressure under trailer of the SV196 vehicle Average pressure under trailer of SOV vehicles
36 kN/m² 98 kN/m² 56 kN/m² 66 kN/m
Table 1. Approximate average pressures for vehicle loads.
Surcharge Analysis Methods There are a number of theoretical methods that can be used for the analysis of surcharge pressures. These methods vary in approach, from some that are b ased on elastic properties [6] [7] (Boussinesq ) to others that are based on slip failures in the soil (Coulomb wedge analysis , [8] Williams and Waite ) and also including some empirical and semi-empirical methods [1] [9] (BD37 , CP2 ). Another family of methods is based on the approach of first modelling the distribution of vertical stresses in the soil adjacent to the wall (there are various ways to attempt this) and then multiplying these by an earth pressure coefficient, based on the theory [10] of Rankine to calculate horizontal earth pressures. Unfortunately there is apparently no single method that alone provides a high level of confidence in modelling the soil and its interaction with the structure accounting for its nonlinear behaviour. For this reason and also to explore the sensitivity of the results to the method used, a variety of methods were considered in developing the simplified surcharge models. This paper focuses on the following analytical methods, illustrated in Figure 2: [7] Coulomb wedge analysis to iteratively determine critical horizontal thrust [10] [6] Rankine method based on elastic vertical pressures from Boussinesq analysis [11] [8] CIRIA C580 method based on Williams and Waite .
Development of a Surcharge Model for Abutments Global effects The theoretical effects of the equivalent LM1 vehicle, the SV vehicles and the SOV vehicles have been considered using the analytical methods in Figure 2, assuming an abutment wall crossing the carriageway. The analysis generally predicts a significant concentration of pressure at the top of the wall, as illustrated in Figure 3 for the equivalent LM1 model and the [10] [6] Rankine /Vertical Boussinesq method.
J Shave, T Christie, S Denton, A Kidd
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Qvehicle
Ph tan
A
Ph tan
Qvehicle
N tan
’
Ph
N tan
’
Ph
N
Gearth N
Gearth
B
Polygon of forces ’
(a) Coulomb wedge analysis Q
v
h
R
v
3
2 R
5
’
h
v
z
r
3Qz
h
v
σ h = K aσ v
where K a = (1 - sin ’) /(1 + sin ’ ).
(b) Rankine with vertical Boussinesq
(c) CIRIA C580 Figure 2. Surcharge analysis methods
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Peak pressure
e c a f r u s w o l e b h t p e D
Figure 3. Distribution of pressures for normal (equivalent LM1) loading (based on K a applied to vertical Boussinesq pressures)
A simple and convenient method for comparing the global effects of the various methods has been used, where envelopes of the total shear force caused by one lane of traffic loading have been plotted at intervals down a simple cantilever wall. The results of this comparison are illustrated in Figure 4 for a d ’ angle of 33 degrees ( K a=0.3). The diagram for SOV vehicles is based on the most onerous SOV vehicle configuration, although similar results are obtained for shorter SOV vehicles. Figure 4 includes the effects of reducing the DAF with depth. For the Rankine/Boussinesq and C580 methods, the pressures were calculated based on the DAF at each depth and then [7] integrated to find the shear force. For the Coulomb wedge method this approach was not directly possible, and so the live loads were multiplied by the DAF, with the DAF based on the depth a third of the way down the wedge being considered. For comparative purposes, the effects of the self weight of the earth have subsequently been subtracted from the Coulomb wedge results.
Figure 4. Comparison of shear forces caused by surcharge loading
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As seen in Figure 4, the global effects for a lane of vehicle loading according to these models can be reasonably modelled by a shear force of 200kN (≈660K a kN) at the top of the wall increasing linearly with depth. Hence the preliminary f orm of the surcharge model for global effects was developed in the form of a horizontal knife edged load (KEL) at t he top of the wall of 660K d kN combined with a horizontal uniformly distributed load (UDL) with a magnitude of 20K d kPa for normal loading, 30K d kPa for SV196 and 45 K d kPa for SOV loading, where K d is the design value of K a for flexible walls or K 0 for rigid walls, based on d’. The effects of SV100 were slightly less onerous but similar to SV196 (the SV 100 vehicle is identical to part of the SV196 vehicle) and SV80 loading were found to be slightly less onerous than normal loading. For design it was considered reasonable to have three levels of loading, corresponding to (i) normal loading or SV80 loading, (ii) SV196 or SV100 loading, and (iii) all SOV vehicles. Figure 4 shows that the C580 method did predict higher pressures than the preliminary model for the SV and SOV vehicles at greater depths, however it was considered that the C580 method was probably more appropriate for small concentrated loads near the wall and could be rather conservative when applied to large vehicles with many axles extending far from the wall. (The other methods considered were generally insensitive to l oads further than about H from the wall.)
Local concentrations of pressure and short walls Aside from the global effects of each lane of traffic loading, there can be some intense peak local pressures associated with wheel loads. These local pressures may be particularly important for segmental structures where high localised earth pressures could be applied to a single precast unit. The Rankine method with vertical Boussinesq pressures was used to investigate the distribution of local peak pressures. These are illustrated in Figure 5 for the example of a SV 196 vehicle with equivalent LM1 vehicles in adjacent lanes. As seen in Figure 5, the local peaks in pressure are mainly confined to the top few metres of soil. This effect may conveniently be modelled using an adjustment to the application of the KEL component of the model that was previously described for global effects. From an analysis of the effects on the most critical metre strip for a variety of load configurations it was found that the model shown in Figure 6 could be used to determine both global and local effects. By applying the KEL component over two 1m-wide strips at the edges of the lane, the effects of the local pressures were adequately modelled.
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600
100
90
500
z = 1.5m 80
z = 0.3m 70
400
) a P 60 k ( e r u 50 s s e r P 40
) a P k (
e300 r u s s e r P
z = 0.5m
200
z = 2.5m
z = 3.5m z = 4.5m
z = 0.7m z = 0.9m
z = 5.5m z = 6.5m z = 7.5m
30
20
100
z = 1.0m 10
0
0
15
16
17
18
19
20
21
22
23
24
25
15
16
17
Distance along wall (m)
(a) Pressures in top 1m of soil
18
19
20
21
22
23
24
25
Distance along wall (m)
(b) Pressures from 1.5m to 7.5m depth
Figure 5. Horizontal pressures for SV196 flanked by equivalent LM1 vehicles using the Rankine / Boussinesq method
Normal Loading
F
h
330K d kN/m
20K d kPa
For normal loading in lanes other than lane 1 these loads may be reduced using the lane factor in EN1991-2
For lane widths W eff narrower than 3m this should by increased by a factor 3m/W eff .
SV 100 or SV196 Loading
330K d kN/m
30K d kPa
SOV Loading
330K d kN/m
45K d kPa
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Figure 6. Horizontal surcharge loading model (characteristic values)
Transverse structural distribution The loads in Figure 6 may be used to model the effects of surcharge loading accounting for the distribution of pressures in the soil. However, for stiff laterally continuous walls the structure itself will have a further influence in distributing the effects of l ocalised pressure concentrations. While the loads in Figure 6 would be appropriate for a complete model of the structure that accounts for the structural distribution, they may be rather conservative for a unit strip approach that neglects the structural distribution. Such an approach is a popular calculation design method for some structure types, and so a further adjustment factor has been developed to account for transverse distribution to allow the model to be used in conjunction with a unit strip approach without undue conservatism. Finite element models were generated to simulate concrete walls of various wall heights and thicknesses. The models were loaded with the pressures generated by the Rankine / Boussinesq method. In general, the results of these analyses indicated that the moments and shears in the walls were almost uniformly distributed across the width of the walls (except at the very top), and that the localised effects of pressure concentrations did not have a significant effect on the distribution of structural effects. By comparing the results of the analyses for walls of various heights, the degree of structural distribution was investigated. This investigation suggests that for a metre strip analysis of a vertically spanning transversely stiff wall, the moments and shears caused by the KEL component F of the loads in Figure 6 may be reduced by the empirically determined factor (1+0.5 z)/(1+ z), where z is the depth below the top of the wall. However, this factor should not be taken as less than 2/3 (which corresponds to the KEL component of total width 2m becoming uniformly distributed over the 3m wide lane). The effects of the UDL component h should not be reduced.
Buried structures The use of a horizontal KEL at surface level to represent the concentration of loading near the surface is an appropriate simplification for structures that are not buried. However, the influence of the concentration of pressures may also affect buried structures where the top of the structure has less than 2m depth of fill. A reduction factor has been developed to be applied to the KEL component F , with the form of the factor based on approximating the pressures in the top 2m to a triangular distribution, as shown in Figure 7. The triangular distribution is consistent with the parabolic variation in shear force towards the top of the wall that can be seen in Figure 4. Hence for structures where the top of the structure is buried but at a depth h (in metres) less than 2m below ground level, F is reduced by a factor
h 1 2
2
and
applied at the top of the structure. For structures buried deeper than 2m, the KEL component F is not applied. The UDL component h is unaffected.
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Horizontal triangular load, F 2m
h
Uniform horizontal pressure, h
Proportion of triangular load applied to wall =
h 1 2
2
Figure 7. Adjustment for buried structures
Development of a Surcharge Model for Wing Walls and Other Earth Retaining Structures The effect of live load surcharge on wing walls is different from that on abutments walls. The lanes are not perpendicular to the wall and so the relative position and orientation of the vehicle loads are different from abutment loading. Wing walls may run parallel to the carriageway or can be set at an angle to the carriageway, and in many cases will be remote from the edge of the carriageway. The geometry of wing walls is also often non-uniform. [2] The method in PD6694-1 for wing walls and other earth retaining structures is based on the [8] method of C580 , and requires superposition of the effect of patch loads associated with traffic loading. For loads that are reasonably close to the wall as illustrated in Figure 8 ( a), i.e. where a H tan 45 d the horizontal thrust is determined from the triangle of forces as shown
2
in Figure 8(b) as:
d
2
Pn Q L tan d Q L tan 45
(1)
where =45+ d’/2. The form of equation (1) is trigonometrically identical to the C580 expression, given in (2): Pn Q L
1 sin d 1 sin d
Q L K a
(2)
J Shave, T Christie, S Denton, A Kidd
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Pn
QL
R
45- d’ /2
(a)
(b)
d
2
a H tan 45
Pn
QL R - d ’
(c)
(d)
d
2
a H tan 45
Figure 8. Method for wing walls
d
2
For loads that are further from the wall so that a H tan 45
CIRIA C580 was not
explicit in how to apply the method. If the model of Figure 8 (a) were used then the active wedge of soil would extend below the bottom of the wall, and the boundary condition at the vertical interface would have changed. In developing the PD6694-1 methodology, two alternative approaches were initially considered. The first was to use the method of Figure 8(a) but disregarding the pressures below the bottom of the wall. The second method (which
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seemed more rational) was to adjust the method with a reduced value of to fit within the wall geometry as shown in Figure 8(c) and (d). This approach gives a thrust of: Pn Q L tan d
(3)
where tan
H
(4)
a
A comparison was carried out for the method in Figure 8(c) and the method in Figure 8(a) but disregarding the pressures below the bottom of the wall. This comparison yielded almost identical bending moments about the base of the wall and comparable shear forces for the two methods. The recommendation in PD6694-1 was therefore to have a minimum value of as illustrated in Figure 8(c), which seems to be a rational and sensible solution. A classical Coulomb wedge analysis would indicate that axles further than a distance of approximately H from the wall do not influence the horizontal thrust, and the methods of Figure 8 (where there is no such limit) are on the conservative side for loads remote from the wall. The practical problem with using the methods in Figure 8 is that the effect of every wheel of every vehicle apparently needs to be superimposed, which can be laborious. A simplification may be made for analysing global effects where the wall is parallel to the carriageway, by considering the effect of each line of wheels of a vehicle or a convoy of vehicles and then summing these effects together with those for any vehicles in other lanes. For the case where the wall is longer than L+2a, where L is the length of the vehicle and a is the distance from the wall to the line of wheels, the horizontal thrust associated with each line of wheels may be modelled by taking the sum of the wheel loads in the line of wheels ( W ) and multiplying by tan d using the method of Figure 8. The average thrust per metre of wall associated with the line of wheels is therefore Pn,ave
W tan Lwall
d
(5)
However, where the wall length does not exceed L+2a (or if there is a convoy of vehicles) then it is necessary to superpose the effects of wheels and to determine the critical vehicle position to give the maximum thrust. An alternative approach would be to develop tables giving the worst average thrust per metre for walls of various lengths and for various distances (a) from the line of wheels to the wall, for each vehicle configuration required. The UK National Annex to BS EN 1991-2 allows the dynamic amplification factor (DAF) for both vertical and horizontal effects to be linearly reduced according to the depth below the ground surface. This means that when applying the model of Figure 8 the pressures at each depth are subsequently multiplied by a DAF that reduces with depth, resulting in a total pressure distribution that is parabolic rather than triangular. However, an acceptable degree of accuracy is generally obtained by using a constant DAF based on the depth d P of the centroid of the triangular pressure diagram in Figure 8.
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Conclusions Methods for analysing the effects of live load surcharges on abutments, wing walls and other earth retaining structures have been developed corresponding to the load models in the UK National Annex to BS EN1991-2. The surcharge models have been incorporated into PD6694-1. The model for surcharge on abutments comprises UDL and KEL components to be applied to the abutment, and is appropriate for a variety of structure types including segmental structures where local pressure concentrations may be critical. To allow more economical unit-strip design of structures that are able to distribute loads transversely, a reduction factor has been derived that is a simple function of the height of the wall. This factor may then be applied to the KEL component. The abutment surcharge model is also appropriate for buried structures, with an adjustment necessary for structures with a depth of fill less than 2m. Recommendations have also been made for modelling surcharge effects on wing walls and other earth retaining structures, and guidance has been developed to facilitate the modelling of these effects.
Acknowledgements The work described in this paper was originally carried out on behalf of the Highways Agency and has been developed for PD6694-1, which is t he responsibility of the BSi committee B/526, Geotechnics. The authors would like to thank t he Highways Agency for permission to publish this paper.
References [1] [2] [3] [4] [5] [6] [7]
[8] [9] [10] [11]
Highways Agency (2001) BD37/01 Loads for highway bridges, TSO BSi (2010) PD 6694-1:2010 Recommendations for the design of structures subject to traffic loading to BS EN 1997-1: 2004 (Draft for comment) BSi (1972) BS 153:Part 3A:1972 Specification for steel girder bridges. Loads Highways Agency (2006) BA55/06 Assessment of bridge substructures and foundations, retaining walls and buried structures, TSO Canadian Standards Association (2006) CAN/CSA-S6-06 Canadian Highway Bridge Design Code, CSA, Ontario. Boussinesq (1885) Application des pot entials a l’etude de l’equilibre et du m ouvement des solides elastiques. Gauthiers-Villars, Paris. Coulomb, C. A. (1776). Essai sur une application des regles des maximis et minimis a quelquels problemesde statique relatifs, a la architecture. Memoires de Mathematique et de Physique presentes a l’Academie Royales Des Sciences, Paris 1773, vol. 7, pp. 343 – 387. Williams and Waite (1993) The Design and Construction of Sheet Piled Cofferdams CIRIA Special Publication 95 IStructE (1951) Civil engineering code of practice no. 2, earth retaining structures Rankine, W. (1857) On the stability of loose earth. Philosophical Transactions of the Royal Society of London, Vol. 147. CIRIA (2003) Report C580 Embedded retaining walls – guidance for economic design , CIRIA, London 2003
