TRANSPORT RESEARCH LABORATORY Department of Transport

Contractor Report 333

THE DESIGN OF LARGE SPAN CORRUGATED STEEL STRUCTURES

by P G Beveridge and M Palmer (Stirling Maynard and Partners)

Copyright Controller HMSO 1994. The views expressed in this publication are not necessarily thoseof the Department of Transport. Extracts from the text may be reproduced, except for commercial purposes, provided the source is acknowledged. The work described in this paper forms part of a .Bridges Engineering Division, DOT funded research programme conducted by the Transport Research Laboratory.

Bridges and Ground Engineering Resource Centre Transport Research Laboratory Old Wokingham Road Crowthorne, Berkshire RG11 6AU

1994

ISSN 0266-7045

Ownership of the Transport Research Laboratory was transferred from the Department of Transport to a subsidiary of the Transport Research Foundation on 1st April 1996. This report has been reproduced by permission of the Controller of HMSO. Extracts from the text may be reproduced, except for commercial purposes, provided the source is acknowledged.

EXECUTIVE SUMMARY

The Department of Transport (DOT) Departmental Standard BD12/88 ‘Corrugated Steel Buried Structures’ is limited to corrugated steel buried structures (CSBS) having spans of up to 8m. A significant number of structures, having spans greater than 8m, have been designed and installed in various parts of the world, notably in North America, and the vast majority of these structures have performed satisfactorily. To examine the potential for extending the maximum span allowed in the DOT Design Standard, Stirling Maynard and Partners (SMP) were contracted to undertake an investigation of the behaviour of CSBS with spans ranging up to 14m. Particular emphasis was put on structures, having spans greater than 7m, incorporating thrust beams. There were three areas of study: a comparison of international methods and design standards; a parametric study of CSBS behaviour using finite elements; and a literature review.

.

The comparison of international design methods and standards included AASHTO ( 1977), AISI (1984), the OHBDC (1983) and the Kloppel & Glock design method (1970): all of these allow the design of large span structures. The use of these design methods has, in most cases, resulted in serviceable structures. However, the methods all incorporate empirical rules and depend upon the adoption of adequate site construction procedures. Comparison of the design methods summarises the critical design criteria (either buckling or seam strength), under dead and live loading conditions, for varying soil stiffnesses and spans.

The Finite Element study used the program CANDE to investigate the behaviour of both ellipse and arch structures. A low profile structure was selected with a large ratio of top radius to side radius, and a 7mm thick steel section with corrugations having a 200mm wavelength and 55mm amplitude. The study included an investigation of the effect on performance of span, backfilling, thrust beam size, the extent of high quality backfill and, for the arch structures, re-entry angle and foundation size. The results of the parametric studies include ring compression, bending and buckling, yielding, deflection and shear force at the thrust beam connection.

The literature review encompassed existing long span structures, field monitoring trials, model tests, and numerical analysis. Only a few CSBS have failed, usually during construction, and the factors attributable to the failures include: poor construction practice; poor or inappropriate backfill specification; use of special features; excessively squat structures; and a failure to appreciate hydraulic load effects.

The study shows that there is conflicting information concerning the behaviour and design of CSBS. This is probably due to the complexity of the soil-steel interaction where prediction of behaviour needs to account for the stress and deflection history of the structure, backfill, and foundation soil. However, the report provides the basis for a practical design method for large span ellipse and arch CSBS. The approach taken by S M P attempts to cover all possible behavioural and failure modes which could develop for a wide range of arch and ellipse configurations. Some simple empirical rules are given which should be applied to the design. These include limitations on: maximum span; maximum top radius; side radius; re-entry angle for arches; geometry; minimum fill quality; thrust beam size; and minimum depth of cover. Finally design requirements are suggested and include checks for seam strength, buckling, thrust beam connection, and allowable deflection.

CONTENTS Page No

1 INTRODUCTION

2 COMPARISON OF DESIGN PROCEDURES

2.1 2.2 2.3

2.4 2.5 2.6 2.7

General American Iron & Steel Institute (AISI) American Association of State Highway & Transportation Officials (AASHTO) Departmental Standard BD 12/82 Ontario Highway Bridge Design Code (OHBDC) 1983 Kloppel and Glock method, as Modified by S M P Direct Comparison of Design Methods

3 FINITE ELEMENT STUDY

3.1 Description of Study 3.2 Findings

4 REVIEW OF TECHNICAL LITERATURE

5 CONCLUSIONS AND RECOMMENDATIONS

6 ACKNOWLEDGEMENTS

7 REFERENCES AND OTHER REVIEW LITERATURE

APPENDIX A - List of Figures - List of Tables

- Notation - Glossary

APPENDIX B - Figures

1

3

3 4

5 7 8

10 14

20

20 22

31

33

38

38

APPENDIX C - Tables

ABSTRACT

This report investigates the behaviour of flexible corrugated steel buried structures of spans ranging between 0.9m and 14m, with particular emphasis upon large span structures, of 7m and above incorporating thrust beams.

The report incorporates a review of design methods, a finite element study of the behaviour of arch and ellipse large span structures, and a review of technical literature encompassing model testing, full scale load testing and finite element modelling.

The report attempts to summarise the basis of a suitable design method for large span ellipse and arch structures incorporating thrust beams.

1 .o

1.1

1.2

1.3

1.4

INTRODUCTION

Stirling Maynard and Partners ( S M P ) were appointed by the Transport Research Laboratory (TRL) in 1986 to continue the development of a design method, for use by the Department of Transport (DOT), for corrugated steel buried structures (CSBS) of larger spans than those allowed in the then current Department Standard BD 12/82, ‘Corrugated Steel Buried Structures’ (Reference 14).

At that stage considerable work had already been carried out to develop a Departmental Standard for large span CSBS with closed inverts using the methods for closed invert structures developed by Dr Glock in Germany (References 18, 19 and 20), and modified by S M P in their reports to Armco Ltd (now Asset International Ltd) and the DOT. The relevant reports by S M P are ‘The Design of Armco Multi Plate Superspan Structures’ July 1979, ‘The Design of Armco Multi Plate Superspan Structures with Worked Examples’ August 1984, and ‘Armco Superspan Design Proposals, Supplementary Information’, 1986 (References 9,lO and 2 1).

The brief was to extend the assessment of the Glock design method (Reference 20) for large span structures and to give recommendations for any adjustments or modifications to the proposals identified above, with special reference to the application to arch structures carried by strip foundations. In particular it was intended that positive advice should be given to define the maximum and minimum angles of re-entry for arches, and to give a proposal for a method of designing the footings, taking into account the effects of differential settlement between the footings and the fill.

Worthwhile areas of investigation and research were identified as follows:

1. A comparison of Design Methods and Standards used elsewhere.

.. 11. To carry out a finite element (FE) study using the CANDE finite element

program, Reference 27, (developed for the Federal Highway Administration, Washington DC) to compare the behaviour of a low profile arch structure with a closed invert ellipse structure. It was also decided to carry out further

1

modelling to study the effects of varying the quality and type of the backfill and the native ground, the effects of varying the foundation sizes for the arch, and the effects of changing the angle of re-entry of the arch from 0" to 25". In addition it was intended to investigate the effects of providing span/2 of selected side fill and a full span of side fill to either side of the structure, and the effects and optimum size of thrust beam.

... 111. To study a wide range of technical papers encompassing theory, model testing

and full scale load testing.

1.5 The work carried out by Glock for closed invert large span structures was perceived to have an advantage over other design methods because buckling behaviour, backfill quality, the shape of structure and cover requirements under live load are all taken into account. Glock has utilised the work on closed invert structures to carry out designs for arch profiles on the basis that the upper part (crown) of the structure is the most critical element of the design in terms of buckling and ring compression, and that this element will not be significantly altered by replacing the invert of the ellipse by strip footings. No modification to the required factors of safety was advocated by Glock, and this was in keeping with the American Association of State Highway and Transportation Officials (AASHTO) Standard Specification for Highway Bridges, 1 2th Edition (1977) design method (Reference 13) which treats the design of arches and ellipses in an identical manner. AASHTO advises that the foundation should not be oversized to avoid differential settlement and draw down effects between the backfill and the structure.

1.6 In contrast the American Iron & Steel Institute (AISI) Products Handbook 1971 (Reference 16) advises that circular arch structures require a larger factor of safety on wall stress and seam strength due to the restraining influence of the footings. The additional factors of safety recommended were between 1.3 and 2. These factors were reduced in the Canadian edition in 1984 to 1 .O and 1.35 as a function of re-entry angle and geometry.

1.7 During the early stages of the project a draft of a possible Departmental Standard for closed invert large span structures was evolved by the DOT, with input from SMP. This standard was used to design and check the adequacy of the Rea Brook Bridge in Shropshire which was an 11.408m span ellipse profile and which subsequently was installed in 1987.

1 -8 During this study, Departmental Standard BD12/82 was revised to become BD12/88. However, only minor amendments were made to the design method and so references made in this report to BD12/82 are equally applicable to BD12/88.

i

2

c

2.0

2.1

2.1.1

2.1.2

2.1.3

2.1.4

COMPARISON OF DESIGN PROCEDURES

General

A significant number of large span structures have been designed and installed in various parts of the world, notably in America and Canada. In section 4 of this report reference is made to reviews of the performance of large span structures, the vast majority of which have behaved satisfactorily. Instances where failures have been reported are studied separately. Such failures appear to be attributable to causes which can be avoided if suitable guidelines are adhered to.

For the vast majority of installed structures the design methods utilised have apparently resulted in an adequate structure. As already inferred, however, the various design methods incorporate empirical rules and depend on sensible and adequate procedures being adopted on site.

The review of the existing design methods considers those used for both large and small span structures. An attempt has been made to extrapolate the design methods for short span structures to see if they can be applied to long span structures. FE methods of analysis have been used by various researchers and designers. Where structures incorporate special features such as thrust beams, FE techniques have been utilised to attempt to verify field observations. FE methods have also been used to? try to establish realistic models for non-elastic soil properties and compaction models.

The design methods reviewed are as follows:

1.

.. 11.

... 111.

iv.

V.

vi.

vii

I.. . -1

American Iron and Steel Institute ‘Handbook of Steel Drainage & Highway Construction Products’ First Canadian Edition (1984) (Reference 1 1).

American Iron and Steel Institute ‘Handbook of Steel Drainage & Highway Construction Products’ Second Edition (1 97 1) (Reference 16).

0:

I

American Association of State Highway and Transportation Officials ‘Standard Specification for Highway Bridges’ (1 969) (Reference 12).

American Association of State Highway and Transportation Officials ‘Standard Specification for Highway Bridges’ (1 977) (Reference 13).

Department of Transport Departmental Standard BD 12/82 ‘Corrugated Steel Buried Structures’, now replaced with BD 12/88 (Reference 14).

Ontario Ministry of Transportation and Communications ‘Ontario Highway Bridge Design Code - Soil Steel Structures’ (1 983) (Reference 17).

Work by Kloppel & Glock, as modified by SMP in their 1979 report (References 19 and 9).

3

2.1.5 A summary of the main features of the various design methods has been given in Table C-1, in Appendix C.

2.2 American Iron & Steel Institute (AISI)

2.2.1 In the AISI 1971 Edition (Reference 16) long span structures are not specifically covered by the design procedures set out. The design procedures set out for circular pipes, elliptical profiles, pipe arches and circular arches (on footings) are based on work sponsored by AISI at Utah State University from 1967 to 1970 under the direction of Dr Reynolds K Watkins, which entailed an extensive testing and monitoring programme.

2.2.2 From this work relationships were established for lower bound buckling failure as a function of compressive stress in the pipe walls, and the stiffness of the pipe wall in bending (EI) for structures embedded in selected backfill compacted to 85% of Proctor Density given in BS1377: Part 4: 1990: Methods 3.3 and 3.4 (Reference 39). Additional checks were included for ring compression in terms of seam strength and yield stress, for the provision of a pipe stiff enough to sustain backfill and handling during installation, and for limiting the earth bearing pressure at the haunches of pipe arches.

2.2.3 In the 1984 AISI Canadian First Edition (Reference 11) the design method is extended to include large span structures incorporating special features. The basis of the design procedure is stated as being work carried out by various workers using FE Analysis, together with Federal Highway Administration Report RD77- 13 1 (Reference 22) summarising the status of Long Span Corrugated Structures.

2.2.4 The section for short span structures remains the same, with the exception of circular arch structures.

Figure 1 Semi-circular arches

O"=Re-entry angle

A reduction in the allowable compressive stress permitted in the pipe wall is required to take account of the fact that the steel ring is restrained at the base of the arch and cannot move into the fill at this point, and to avoid the risk of column type buckling.

4

The required reduction factors are as follows:

AISI AISI 1971 1984

i

Semi-circular or less e I 00 2 1.33

Re-entrant arch 00 < e I 200 2 1 .o

Re-entrant arch 200 c e I 300 1.33 1 .o

Re-entrant arch 0 > 30" 1 .o 1 .o

Where height of fill is less than span, ring compression is calculated as overburden pressure multiplied by radius.

2.2.5 In the 1984 AISI Canadian edition (Reference 11) the analytical design rules for large span structures relate to seam strength only. Design ring compression is calculated on the basis of overburden pressure multiplied by top radius, and a factor of safety of 2 is required on ultimate seam strength values.

Buckling and deflection criteria are deemed to be satisfactorily catered for providing the following measures are adopted:

1. Provision of thrust beams. b .

11. For height of fill less than 3.6m backfill complying with AASHTO specification M145 Table 2 Class A-1, A-3, A-2-4 or A-2-5 should be used and must be placed in balanced layers and compacted to at least 90% of optimum density to the AASHTO compaction test, reference T180. The compactive effort utilised within this test is virtually identical to that in BS1377: Part 4: 1990: Methods 3.5 and 3.6 (Reference 39), which give a slightly greater compactive effort than Clause 3.7 in the same British Standard. For heights of fill greater than 3.6m backfill compliance with Class A- 1, A-3 soils compacted to 90% of T180 is required.

.* ..

... 111. Care must be taken to avoid excessive deflection occurring during backfilling.

iv. Selected side fill should extend a minimum distance of 1.8m from the sides of the structure if the embankment material is of good quality well compacted material, and a minimum distance of 0.6m to 1.2m above the structure.

2.3 American Association of State Highway and Transportation Officials (AASHTO)

2.3.1 The AASHTO requirements for design prior to 1977 differentiate between short span structures and large span structures with acceptable special features.

5

2.3.2 The design for short span structures (AASHTO 1969) is based on the use of selected backfill within specified grading limits compacted to 90% of the optimum dry density to the AASHTO T90 compaction test. Test T90 is identical to BS 1377: Part 4: 1990: Methods 3.3 and 3.4 (Reference 39), which are the Proctor density tests. Ring compression was calculated by multiplying crown pressure by s p d 2 and checks were required for buckling, seam strength deflection and handling stiffness. A factor of safety of 2 is required for buckling and 4 for seam strength.

2.3.3 Long span structures are designed using the same method for calculating ring compression but providing an acceptable special feature is adopted (one of these being thrust beams) no check is required for buckling, deflection or handling stiffness. Again selected backfill is specified compacted to 90% of density to test T90.

2.3.4 In the 1977 and 1979 revisions the method for calculating ring compression is altered for large span structures by substituting top radius for s p d 2 in the equation. At the same time the required factor of safety on seam strength is reduced from 4 to 3 for all structures, and compaction of backfill to long span structures increased to 90% of the optimum dry density to the AASHTO T180 compaction test. The minimum extent of selected backfill for large span structures is also increased from 3.66m to the greater of s p d 2 or rise x 213.

2.3.5 For heights of fill less than 3.66m for large span structures selected backfill complying with AASHTO gradings A-1, A-3, A2-4 or A-2-5 are permitted, whilst for heights of cover in excess of 3.66m backfill has to comply with gradings A-1 or A-3. For the largest structure permitted, with a top radius of 7.62m, a minimum height of cover 1.2m is specified for American highway loadings, corresponding to approximately s p d l 0 .

2.3.6 Long span structures complying with above requirements do not need to be checked for buckling, deflection or handling stiffness.

2.3.7 The 1977 amendments take account of practical experience gained in the construction of long span structures and are considered to represent a sound empirical approach to the design of these structures. Additional requirements include limitations to the geometry of long span structures for a variety of profiles including horizontal ellipses, low profile arches, high profile arches and inverted pear profiles as follows:

Maximum plate radius: 7.62m Maximum central angle of top arch: 80" Minimum ratio of top arc radius to side arc radius: 2 Maximum ratio top arc radius to side arc radius * : 5

* A high ratio to be avoided when significant heights of fill are involved.

2.3.8 No modification to the design procedures is incorporated for arch structures classed as small span or larger span structures.

6

2.3.9 For the design of single radius arches, however, the rise to span ratio is limited to between 0.3 and 0.5. The corresponding foundation design is discussed and advice given that it is undesirable to make the metal arch relatively unyielding or fixed compared to the adjacent side fill. The use of massive footings or piles to prevent settlement of the arch is generally not recommended. The footings should be.designed to give uniform longitudinal settlement of acceptable magnitude. Allowing provision for the arch to settle will protect it from possible overloading drag down forces generated by settling of adjacent side fill.

2.3.10 The second consideration is the allowable bearing pressure of the soil under the footings coupled with the applied loadings on the base. The footing reaction for the metal arch is considered to act tangentially to the metal plate at its point of connection to the footing, the value of the reaction being the thrust in the metal arch plate at the footing.

2.3.11 Work has been carried out by S M P to try to relate the grading limits in AASHTO for selected backfill around corrugated steel structures to an equivalent lower bound value of constrained soil modulus, M'.

The results are shown below:

Lower Bound Values of Constrained Soil Modulus M*

Grading 90% Compaction to T90 90% Compaction to T180

s. 3

A-1, A-3 - 35,000 --> 45,000kN/m2 A.

A- 1 ,A-3,A-2-4, - 30,000 --> 4 1 ,000kN/m2 4 A-2-5 . a

A-I, A-3, A-2 23,6 5 OkN/m2 28,000 --> 38,000kN/m2

2.4

2.4.1

2.4.2

2.4.3

Department Standard BD12/82

The scope of the Departmental Standard (Reference 14) is limited to closed invert structures with spans of between 0.9m and 8.0m. Ring compression is calculated on the basis of bulk density times height of cover plus top radiusl4, all multiplied by span/2. Live loading crown pressure is calculated on the basis of an assumed spread of load from wheel contact areas acting at crown level, multiplied by top radius.

Buckling checks are carried out on the basis of work by G C Meyerhof et a1 (References 3,4 and 6) . Buckling strength reduces with reducing height of cover. An adjustment to the theoretical transverse elastic buckling stress, fb, is carried to allow for imperfections of the pipe wall.

Classes of acceptable soil are specified together with lower bound values of M' (constrained soil modulus) for various degrees of compaction. In the later version of

7

the standard (BD12/88) greater flexibility is given to the designer by permitting the use of high quality backfill giving higher values of M' which can be used in the design. Guidance is given as to how to measure the values of M'.

2.4.4 Design checks are also carried out for deflection, ring compression, pipe yielding, handling stiffness and the durability of the steel. Overall factors of safety of 2.0 are provided for buckling and pipe yielding and 3.7 for seam strength and 4 for deflection. Allowance for metal loss and durability over a 120 year design life is achieved by following rules for estimating metal loss after the breakdown of protective coatings. The buckling theory used is considered by some researchers to be conservative, but for the range of structures considered ring compression is thought to be the critical failure mode, rather than buckling at all except the largest spans included.

2.5 Ontario Highway Bridge Design Code (OHBDC) 1983

2.5.1 The OHBDC (Reference 17) was first described with respect to the sections dealing with soil structures in a paper by Abdel-Sayed and Bakht published in 1981 (Reference 15)' and was formally introduced in 1983.

2.5.2 The design code was formulated by a task force of engineers and scientists representing industry, universities and governments throughout North America.

2.5.3 Account was taken of previous theoretical work and practical experience. It was realised that not all the experience and knowledge from previous successful installations of large span structures could be readily synthesised into precise mathematical terms for general application by designers.

2.5.4 Reference was made to the work by Marston-Spangler (References 29 & 30), White and Layer (Reference 3 1) (ring compression theory), Kloppel and Glock (Reference 19), (as also outlined in SMP's 'Report on the Design of Armco Multi-Plate and Superspan Structures' 1979, Reference 9) and FE studies, as well as established practice.

2.5.5 Of particular note is the allowance in the code for modelling of soil arching above buried structures. This gives significant reductions to ring compression due to dead loading as a function of height of cover and the aspect ratio of the span and top rise of the structures. The design charts presented are based on FE studies using CANDE.

2.5.6 For the range of long span structures considered in our study the aspect ratio D,/ D, is normally inside the range 1.45 to 1.70. For the "squatter" structures with a high aspect ratio at a height of cover of 2m, a shape factor p of 0.65 is given, whilst for an aspect ratio of 1.45 a p of 0.78 is indicated. Ring compression is then calculated on the basis of p times top radius times overburden pressure. A factor of safety of 1.66 is then applied to ring compression.

-

2.5.7 With respect to buckling criteria the code considers two distinct zones in the structure, the crown where the pipe wall is subjected to active earth pressures and deflects away

8

from the fill and applied loading; and the lower portion of the structure where predominating passive earth pressures are generated and the pipe moves into the side fill. The angle 8" defining the upper zone is 40 degrees.

I /"TIAL SHAP€

UPPER ZONE TANGENTIAL MOVEMENT OF ENDS CONSIDERED

I I I I I I I I I I I I i ! ,POINT OF ZERO I

LOWER ZONE TANGENTIAL MOVEMENT OF ENOS NEGLECTED

Figure 2 Demarcation of two buckling zones

2.5.8 For the lower portion of the pipe buckling theory in line with the findings of Meyerhof et a1 (1963), Watkins (1 966) and AASHTO (1 977) are adopted. (References 4, 38 and 13)

2.5.9 The upper portion of the pipe is considered in the light of the work of Kloppel and Glock (References 18 and 19). Account is taken of the tangential movement of the pipe wall (resulting from settlement of the lower portion of the structure) in deriving a modification factor for the buckling equation formulated for the lower portion.

2.5.10 There is a facility for providing a different gauge of metal for the upper and lower portions of structures, with the upper portions requiring the greater thicknesses.

2.5.11 Provision is included for circular arch structures on footings. Non re-entrant circular arches attract approximately 14% more dead load than a closed invert circular profile with a height of cover of 2m, and 23% more with a height of cover of 6m.

2.5.12 A minimum extent of side fill of s p d 2 is required for both short and long span structures. Suitable values of soil stiffness are suggested for use in the buckling equations as a function of grading classification. Compactive effort for both short and long span structures is 85% to 95% of Proctor density.

9

2.5.13 Deflection criteria are not considered but empirical rules are given for minimum height of cover.

2.5.14 The required factors of safety for buckling and yield stresses are 1.56 for dead load and 1.87 for live load.

2.5.15 Handling and installation strength are considered by limiting the stiffness of the pipe wall as a function of pipe diameter.

2.6 Kloppel and Glock Method, as Modified by SMP

2.6.1 Kloppel and Glock (References 18 and 19) investigated the problem of trying to arrive at a rational design method for buried flexible structures at Darmstadt University in Germany.

2.6.2 Their work was published in 1970 (Reference 18) and concentrated upon circular and pipe arch profiles of up to seven to eight metres in span. The work took account of the observation that in the upper pipe zone the crown tends to deflect away from the applied loadings whilst in the lower pipe zone pressures are generated by a combination of active and passive earth pressures, where the structure tends to deflect into the fill material. A model for the distribution of active earth pressure was postulated as a function of the height of cover above the structure and the ratio of applied surface live loads to applied crown pressure due to dead loads.

. A c t i v e e a r t h - pressures.

.Passive e a r t h - pressures.

1 L O W F I L L '4 6 - 90'

HIGH F I L L Y 8 - 135'

Figure 3 Active and Passive Soils Pressure Zones

2.6.3 The lower portion of the pipe was then modelled as a bend resistant frame on spring supports, whilst the crown was considered as an elastically embedded, elastically supported and elastically restrained two pin arch. Kloppel and Glock reasoned that the top portion of the pipe was more vulnerable to buckling type failure. Load applied in increments to the model permitted the derivation of the spring stiffnesses at the crown supports to be established, and enabled the crown pressure necessary to cause a snap through buckling failure of the crown to be derived, using an energy method.

2.6.4 Further models were investigated including a three pin arch, the effects of ignoring

10

bending resistance in the lower part of the pipe, and the effects of development of friction at the interface between the soil and the pipe wall.

2.6.5

2.6.6

2.6.7

E t a s t i c a l l y bedded and supported

three -h inged a r c h as a subst i tu te

s y s t e m for the upper a r e a o f pipe

E l a s t i c a l l y f ixed sprocket c h a i n

as s u b s t i t u t e system for the

lower a r e a of p i p e f o r t h e

A c a l c u l a t i o n of the s u b s t i t u t e

spring r i g i d i t y .

( N e g l e c t i n g p l a s t i c h i n g e s . )

n

Figure 4 Structural Model of Pipe Arch

For structures where pipe stiffness EI/CR," (defined by wall stiffness divided by a soil stiffness, and pipe radius to the power of 4) is small, which is the case for longer span structures, the solutions converged and Kloppel and Glock conclude that the solution ignoring bending stiffness in the lower pipe gave a reasonable lower bound solution. The results of their two dimensional frame and crown stability calculations are summarised in graphical form for alternative geometries and height of cover conditions, as a function of crown pressure causing failure against pipe stiffness. Information obtained from the analysis includes the ring compression in the pipe wall coincidental with buckling failure, and deflection of the pipe crown relative to its supports coincidental with buckling failure. These results are also presented graphically.

Although the phenomenon of soil arching was recognised as an effect which would tend to occur in reality under dead loading, Kloppel and Glock take the view that there was insufficient information available at the time to quantify the effect, and therefore the total applied crown loadings were not reduced in any way as the crown deflected away from the loading. 4

The values of ring compression predicted by the theoretical results are always in excess of the initial top radius multiplied by the predicted crown pressure necessary to cause buckling failure. This is because the supports for the crown section move tangentially during the loading sequence as the lower part of the pipe deflects into the fill, resulting in an increase in the top radius of the pipe. To maintain equilibrium a

11

corresponding greater ring compression must be developed to support the applied pressure.

2.6.8 In order to carry out a design using their results Kloppel and Glock advocate use of a factor of safety of 2 on buckling, with a check to establish that the co-incidental ring compression does not exceed the ultimate seam strength of the pipe wall. Although a factor of safety of 2 is therefore also implied for ring compression, it is in fact in excess of this value when calculated on the basis of ultimate seam strength divided by ring compression (yHRT) at working load conditions, due to the deformed shape of the structure at ultimate load conditions, where:

y = bulk density of fill material H =

RT= height of cover above the top of the crown radius of the corrugated plates forming the crown of the structure

2.6.9 Kloppel and Glock also investigate the effects of backfilling upon ring compression and the bending moments developed in the pipes during placement and compaction of the fill. By modelling the pipe as a frame subjected to horizontal compaction pressures they conclude that the thrusts developed were small, and that bending moments tended to be of the opposite sign to those developed by dead and live loadings in the completed structure. These are therefore not taken into account in the buckling or ring compression checks, but are considered in a further investigation which they carried out. Compliance with empirical rules for handling stiffness is advocated.

2.6.10 Soil failure under live loading at low fill cover is considered. A failure mode involving the downward movement of a block of earth beneath the surface load causing an inward buckle of the loaded part of the crown and a consequent outward deflection of the unloaded part of the crown and the adjacent body of earth is postulated. The bending resistance of the pipe wall is added to the shear resistance of the soil body to arrive at predictions of maximum live loading as a function of the internal angle of friction of the fill, and the bending stiffness of the pipe. The bending moments generated during backfilling are taken into account to reduce the bending resistance of the crown.

2.6.1 1 Kloppel and Glock carried out a series of laboratory model tests in which the pipe was modelled by steel rings and the fill by foam rubber. Good correlation with their theoretical predictions is claimed. In addition two full scale load tests were carried out in which the load capacity of the structures tested exceeded those predicted by their method.

2.6.12 In Dr Glock’s 1973 Superspan report to Armco (Reference 20), he reports upon his application of the same analytical techniques used for pipe and pipe arches for Armco Superspan structures incorporating thrust beams.

2.6.13 In th is work Glock again differentiates between the upper and lower portion of the structure in terms of response and susceptibility to buckling, and models the effects of the thrust beam by including its presence into the frame model for the lower part

12

of the structure.

Y The s t i f f e n i n g ef fect of the thrust beam i s taken in to account

using the s t a t i c system shown belov, and the t o t a l subs t i tu te

spring r i g i d i t y Cers and aperture angle 200 can be found.

Point o f zero radial de f l ec t ion

I , E l a s t i c a l l y bedded bend

resistant polygonal l y

curved b e a m .

Figure 5 Glock Superspan Model - 3

1

2.6.14 The size of the thrust beam assumed in the analysis is somewhat greater than the

2.6.

2.6.

standard sizes traditionally adopted by Armco. The height of the vertical face of the thrust beam is taken as 0.19 times the top radius in the analysis. The effects of this are discussed in section 3. A

"L

5 The zones of active earth pressure assumed, which have a significant effect upon the response of the lower portion of the structure, are as before for low cover and-high cover conditions.

6 A range of elliptical profiles are commercially available with varying span to rise ratios and varying ratios of top radius to side radius. To take account of this, parallel calculations are carried out for two distinct geometries, these being defined as top radiudside radius equal to 2.45 for profile type A and top radiudside radius equal to 3.65 for profile type B. As might be expected for profile type B, which is the "squatter" profile, higher tangential movements appear to occur at the thrust beam position causing crown instability at lower crown pressures than for an equivalent type A structure with the same top radius.

2.6.17 The work by Dr Glock modelled elliptical, closed invert structures. ' We are aware, however, that Dr Glock considered his design graphs could be equally well applied to arch structures and this facility is included in the Stirling Maynard and Partners 1979 report (Reference 9), together with modifications to the design method to comply with British Standards for determining live loading effects, and for defining the demarcation between a high cover installation and a lower cover installation.

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2.7 Direct Comparison of Design Methods

2.7.1 In order to permit a direct comparison of the various design methods, calculations have been carried out for all the above design methods for circular, ellipse type A profiles and ellipse type B profiles for spans ranging between 4m and 16m. To illustrate the treatment of live loads and dead loads by the various methods, live load capacity at a height of cover of 1.5m was calculated, and maximum height of cover without any live loading was calculated. For both load conditions values of constrained soil modulus of 33,000kN/m2, 66,000kN/m2 and 1 00,000kN/m2 have been utilised where there is a facility to incorporate a value of soil stiffness into the assessment for buckling strength. For simplicity the use of 152mm x 51mm corrugated plate 7mm thick is assumed throughout. The demarcation between short and long steel structures has been assumed to occur at a span of 7m.

2.7.2 The following criteria are shown for a range of spans, in graphical representation for each design method, where they form an integral part of the method:

i. Yielding of corrugated plates 11. Buckling of corrugated plates iii. Seam strength failure iv. Horizontal deflection

..

2.7.3 Structures subject to live loading

AASHTO: The controlling failure mode for all elliptical spans of greater than 5.5m is seam strength whether 2 or 4 bolts per corrugation are utilised. Without the incorporation of thrust beams and the requirement to increase compactive effort and backfill quality, buckling would have become the controlling factor at a span of 7.3m to the 1977 design rules, and 9.7m to the 1969 design rules. Under 45 units of HB loading taken from DOT Departmental Standard BD37/88 (Reference 25) and distributed in accordance with British practice, spans of 8.9m could be achieved to the 1977 rules for "short" span structures and 11.8m to the 1969 rules for "short" span structures.

The requirements for higher quality fill and the use of thrust beams in both sets of rules effectively prevents buckling from becoming the most critical failure mode, this being seam strength. By back calculation from the soil modulus stated, the constrained soil modulus (MO) assumed in the buckling equation for short span structures is approximately 23,650kN/m2. It has been estimated that the lower bound values for constrained soil modulus for selected backfill to long span structures is between 30,000kN/m2 and 40,000kN/m2 for covers of less than 3.6m. Strict application of the design rules permits long span structures of up to 12.5m with 2 bolts per corrugation and in excess of 12m for 4 bolts per corrugation on the basis of seam strength criteria. The results show that circular profiles can carry significantly higher loading than profile A ellipses, which in turn can carry more than profile B ellipses.

OHBDC. For both circular and elliptical profiles buckling failure of the structure crown appears to be critical for all heights of cover. The graphical results suggest that

14

c

long span structures designed to this code would be incapable of carrying 45 units of HB loading, and that at a height of cover of 1.5m spans in excess of 9.5m would be incapable of carrying live loading. Since this is clearly at variance with observed behaviour it is concluded that if the code has been correctly interpreted, it is excessively conservative for buckling criteria at low cover and large spans. No provision is given in the code to take account of the thrust beams.

BDI2/82: As with the OHBDC buckling is always the critical failure mode for design and typical elliptical spans in excess of 7.82m appear to be unable to carry 45 units of HB loading, whilst there is no significant live load capacity remaining at spans in excess of 1 lm. Again this suggests, on the basis of observed behaviour, that for spans in excess of 8m the extrapolated buckling requirements appear to be unduly onerous.

SMP/Glock: For elliptical structures buckling is always the critical factor for M* values of 33,000idrJ/m2 or less, and if 4 bolts per corrugation are provided buckling remains the critical factor for M' values of 66,000kN/m2.

For profile types A & B constrained soil moduli of 33,000kN/mZ impose serious limitation on the live load carrying capacity of the structures and a minimum value of 40,000kN/m2 seems appropriate to ensure reasonable live load carrying capacity. If metric corrugations with a wave length of 200mm are utilised the situation will be further improved.

The calculated values for seam strength criteria are based on the Glock design method and give slightly more stringent requirements than the factor of safety of 3 on ring compression calculated on the basis of yHRT as described in section 2.6.8.

Use of M' = 100,000kN/m2 effectively precludes the possibility of buckling; type failure for long span structures being critical at low heights of cover. Seam strength with 4 bolts per corrugation then becomes the critical failure mode.

.?,

,

Circular profiles exhibit superior load carrying capacity compared to profile A ellipses which in turn can carry more loading than profile B ellipses.

AISI 1984: This design method requires fill of a minimum quality be provided and compacted to the same standards as AASHTO 1977, and that providing this is carried out for long span structures with thrust beams no check is required for buckling type failure. Since the factor of safety required by AISI for seam strength is 2, compared with a factor of safety of 3 by AASHTO, this design method allows the longest span structures and most heavily loaded structures of all the design methods considered.

Direct comparison of SMP/Glock andAASHT0 I977 Modification to the AASHTO requirement in 1977 gave rise to less optimistic predictions of carrying capacity as compared to the 1969 design rules. For plates with 4 bolts per corrugation AASHTO (1 977) always gives a more optimistic prediction of live load capacity than SMP/Glock utilising values of constrained soil modulus of M' of approximately 80,000kN/mz or less (see Figures B1 and B2 in Appendix B).

15

Given that the lower bound limit for values of constrained soil modulus required by AASHTO for selected fill to large span structures lies within the limits of 30,000kN/m2 to 41,000kN/m2 and that this design method appears to have proved suitable for the vast majority of structures installed prior to 1977, it would appear that Glock's predictions of buckling strength may be pessimistic by a factor of approximately 2.

2.7.4 Structures subject to dead loading only

AASHTO: Our findings indicate that with the AASHTO design criteria for ellipse profiles, seam strength is the critical mode of failure in design, and that for the corrugated plates described, significant heights of cover in the order of 6m can be supported if 4 bolts per corrugation are utilised for structures of about 12m span. This holds true for both the pre and post 1977 rules.

Extrapolation of the small span buckling criteria applied using top radius, rather than span/2, shows there would be a dramatic reduction in load carrying capacity if a high quality fill placed with greater compactive effort were not specified for long span structures incorporating thrust beams. The soil modulus used as a lower bound value for small span structures is apparently in the order of M' = 23650kN/m2. Our assessment of the AASHTO requirements for grading limits for heights of cover greater than 3.6m, is that the lower bound value of constrained soil modulus for these soils compacted to 90% of test T180 lies between 35,000kN/m2 and 45,000kN/m2.

OHBDC: The graphical results for the OHBDC requirements under dead loading only show a marked increase in load carrying capacity as compared with structures at low cover conditions under live load, and strict application of the code would appear to permit 6m of fill up to a maximum span of over 13m.

Buckling is still always the failure mode controlling designs. The relatively low factor of safety required for seam strength makes this criterion much more optimistic than when predicted by AASHTO. Yield of the pipe wall becomes the governing factor rather than seam strength if buckling were to be ignored.

For economical design, use of this code would permit thinner gauges than AASHTO.

On a practical point, however, there could be some difficulty in constructing a 13m span ellipse if calculations for intermediate height of cover during the construction stage show failure could occur whilst fill is being placed, which would appear to be the case.

B012/82: Our results indicate that for spans of up to about 7 to 8m reasonably significant heights of fill are permitted for circular profiles and, to a degree, for elliptical profiles. Buckling criterion for ellipse profiles becomes a controlling and very restrictive criterion, however, with increasing span. Ring compression criteria would limit spans carrying 6m of fill to 10m. Only 4.5m of fill can be carried by a 12m span structure.

16

c

Again the extrapolated buckling criteria for large span structures appears to be v e y pessimistic in the light of the performance of structures which have been satisfactorily installed.

SMP/Glock: If 4 bolts per corrugation are utilised, buckling is the critical failure mode for ellipse profile Type B, and for ellipse profile type A for spans of less than 9m.

The use of M’ values in excess of approximately 100,00OkN/rn’ in conjunction with 4 bolts per corrugation will cause seam strength to become the controlling failure mode, rather than buckling.

AISI (1984’: Due to the low factor of safety on seam strength required. and because no check against buckling is required for long span structures with thrust beams and carefully selected fill compacted to 90% of density to AASHTO test T180, this method permits the use of long span structures to greater spans and under much higher loadings than any of the other design methods. Thus for a 12m span structure a maximum height of cover of 8.3m can be carried, with yield being the failure mechanism critical to the design of ellipse profiles.

It is interesting to note that the soil specification is identical to that in the AASHTO 1977 requirements, giving a probable lower bound M’ value of 35,000kN/m2 to 45,000kN/m2, thus indicating an even greater confidence by AISI that buckling is not a controlling factor, even when the factor of safety on seam strength is reduced.

Direct comparison of SMP/GIocli and AASHTO 1977: Figures B3 and B4 indicate the critical failure modes for each design method at M’ values of 33,000, 66,000 and 1 O0,000kN/m2 (Glock method).

For high cover conditions it is possible, using the Glock method, to obtain a slightly more optimistic design for load carrying capacity for ellipse type A profiles for spans in the range of 8m to 12.5m than when using the AASHTO design method. The AASHTO criterion is dictated by applying a factor of safety of 3 to seam strength, when ring compression is calculated on the basis of yHR,. This does not apply to ellipse type B profiles where the Sh4P/Glock design method always predicts a lower load carrying capacity. If the lower bound M* values, attributable to fill complying with the AASHTO specification of 35,000kN/m2 to 45,000kN/m2, are utilised in conjunction with the SMP/Glock buckling criteria for type A profiles it can be seen that this will always give a lower prediction of load carrying capacity than AASHTO. At spans of 7m the Glock buckling criteria has a much more onerous effect on load carrying capacity than at spans of 12.5m. For both profiles type A and B Glock’s buckling criterion is the controlling factor for M’ of less than 45,000kN/m2. In the light of the structures which have been successfully installed this suggests that at spans of 7m and under the Glock buckling criteria may be excessively conservative, whilst at spans of 12.5m it is more realistic.

17

2.7.5 General Comparison of Design Methods

Of the methods considered, the AASHTO 1977 method is perhaps the best yardstick since it was written on the basis of field experience and is known to be fully compatible with the Armco design methods which have been successfully applied to numerous structures.

The back calculation of the minimum values of constrained soil modulus which are likely to be achieved by compliance with the AASHTO specification for large span structures suggest that the buckling limitation derived from the SMP/Glock method are pessimistic, particularly for low cover installations subjected to high live loading. The buckling prediction may become less pessimistic as spans increase towards 12m and above.

Buckling predictions by extrapolation of BD12/82 and OHBDC (both of which ignore the provision of thrust beams) suggest a very rapid decay in buckling strength with increasing span for high and low covers. By comparison it should be noted that the Glock method predicts very gradual decay in buckling strength with increasing span. The soil arching phenomenon derived from FE studies and incorporated into the OHBDC means that at high fills, use of the code apparently permits the design of highly loaded structures of up to 13m in span. By contrast under low covers subjected to live loading, both codes would effectively rule out many structures which have been installed and which have performed satisfactorily.

The AISI 1984 method and the OHBDC both permit the use of very low factors of safety on ring compression (2 and 1.7 respectively). In the former case this enables a l/3 reduction in seam strength requirements compared to AASHTO, but with the same AASHTO requirements for bacWil1 quality and compaction being applied. The buckling criteria in the OHBDC for the crown appears to be consistently the controlling factor in determining load carrying capacity.

The Glock method always gives more pessimistic results for load carrying capacity, based on ring compression, than AASHTO for all conditions except for ellipse profile type A at high cover. The seam strength provision in the OHBDC and AISI 1984 may prove to be perfectly satisfactory, however it is considered prudent to provide the same factor of safety of 3 as adopted by AASHTO 1977 and the Armco design method (Reference 9) both of which have largely proven satisfactory.

The Glock method has buckling as the controlling factor for all M' values of less than 1 00,000kN/m2 for high cover installations, and 90,000kN/m2 for low cover installations. In order to avoid large span structures being installed with an M' value of less than that recommended by AASHTO (which would be possible if the structure is lightly loaded) the following lower bound values of M' are proposed:

18

Proposed AASHTO Probable Limits

low cover installations M' 2 40,000kN/m2 30,000-->40,000kN/m2 (height of cover less than 3.5m)

high cover installations M' 2 45,000kN/m2 35,000-->45,000kN/m2 (height of cover greater than 3.5m)

Deflection was not a significant factor for large span structures for any of the methods considered, and it does not seem appropriate to incorporate such a check. Of far greater importance is the need to cany out the erection and backfilling in a careful and controlled manner, and to avoid excessive deflections during backfilling. Guidance given by Armco, AASHTO and AISI suggests that the profile dimensions, including deflection under self weight should not deviate more than 2% from the original span and rise. There is a general agreement that the backfill should be compacted to make the structures peak. Armco preferred that after placement of the fill, the crown should not be lower than its intended design position.

Handling limits are a function of previous experience by the manufacturers, and it appears that for large span structures the plate stiffness and thickness required for final design considerations are usually adequate for handling and deflection under self weight. Nevertheless the empirical rule established by Armco for Superspans could be incorporated into a design check. E

Yield stress criteria for the plate are not considered to be a controlling factor, however, future plate and bolting configurations may alter and it would be prudent to incorporate a check for yield stress based on ring compression for yHRT and a factor of safety of two, in keeping with the other design methods. +

It is worth commenting that the Glock design graphs are suitable for a limiting value of EI/CR4, of not less than 0.00005, where:

E I C RT

= Young's modulus of steel (kN/mz) = 2nd moment of area of structure w a l l h i t width (m3) = Soil bedding coefficient (kN/m) = top radius of structure (m)

In conjunction with plate of 6" x 2" (1 52 x 5 1 mm) corrugation, 7mm thick, this limits maximum top radius to 8.23m for low cover installation (M' = 40,000kN/m2) and to 7.9m for high cover installations (M' = 45,000kN/m2). The corresponding maximum spans for the values of top radius are 13.0 to 12.1 8 and 12.5 to 11.70m, for profile types A and B, respectively.

An anomaly of this restriction is that when at these limits, spans may increase if soil stiffness is reduced. Logically an increase in soil stiffness should increase buckling load carrying capacity. In reality, however, this limiting ratio of EI/CR," tends to give an envelope of load carrying capacity which is not significantly less than the seam strength criteria. (Figures B-1 to B-4).

19

It should also be remembered that use of stiffer corrugations will also help to increase the span and top radius limits. For 7mm thick metal in 200- corrugations maximum top radius will increase to 8.39m for low cover installations and 8.36m for high cover installations. These translate into maximum spans of 13.7 to 12.86 and 13.2 to 12.38m respectively for profile types A and B. Thus for a conservative general rule it can be stated that the method is suitable for spans of up to 13m for all types of installation.

A minimum height of cover restriction of span/lO is imposed by AASHTO together with a maximum span limit of 12m for 6" x 2" (152mm x 51mm) corrugations.

3.0 FINITE ELEMENT STUDY

3.1 Description of Study

3.1.1 The purpose of the FE study was primarily to investigate any difference in behaviour that might occur, under dead loading only, between arches and ellipses. It was considered probable that if differences in behaviour did occur above spring line level, then these were most likely to be brought to light by comparing a low profile arch with an ellipse, since with such an arch profile there is the least scope for the side plates near the spring line to deflect into the fill without developing restraint from the foundations. This view appears to be supported by the work and findings in the Federal Highway Administration Report FHWA-RD-79-115 (Reference 26). The structure geometry and general meshes adopted are shown in Figures B-5 and B-6.

3.1.2 The FE programme used for the study was CANDE. Specified runs were carried out by Thorburn Associates, in Glasgow, who have carried out previous work in this field for the Department of Transport (Reference 28).

3.1.3 To allow direct comparisons to be made, the structures modelled have identical geometry above the spring line in terms of span, side radius and top radius. In order to examine structures which other design methods would suggest are likely to be most at risk from buckling type failure, a low profile structure was selected with a large ratio of top radius to side radius. The geometry complies with an Armco structure type reference 45-E-14. The section properties of the corrugated steel are based on 7mm thick 200mm corrugations with 55mm amplitude. A range of fill properties, native soil properties and foundation sizes were investigated.

3.1.4 The structure profile selected is 1 1.02m in span with a top radius of 7.54m and a side radius of 1.85m. The re-entry angle for an arch of this geometry, which is normally commercially available, is approximately loo, and is the minimum angle which manufacturers normally provide.

3.1.5 The thrust beam size specified for the majority of the runs was 0.9m (height of vertical face) which complies with the standard size recommended by Armco. This corresponds to a ratio of 0.1 2RT, as opposed to the ratio of 0.1 9RT which was adopted by Dr Glock in his work on long span structures.

20

3.1.6 Foundation sizes and geometries were calculated using the following measures:

1. At working loads

0 ring compression equal to W/2 acts tangentially on the base,.where W is the total soil load above spring line level.

0 overburden pressure acts co-incidentally on the buried horizontal face of the footing.

0 active earth pressure acts co-incidentally on the outer vertical face of the footing.

0 horizontal forces are resisted by fiction at the underside of the footing.

0 a factor of safety of 3 is required on bearing pressure calculated on the above assumption, against ultimate bearing pressure calculated using Terzaghi’s methods for calculating allowable bearing capacity of strip footings (Reference 23).

.. 11. At ultimate loads **

* 0 ring compression is equal to thrust in the bottom plates as predicted by

Glock, modified if applied crown pressure is less than half of the theoretical ultimate pressure necessary to cause buckling.

c 0 earth pressures remain the same as for working loads.

the ultimate bearing pressure calculated using the above criteria should .”

0

be greater or equal to the ultimate bearing pressure calculated in accordance with Meyerhof s (Reference 23) equation for footings subject to inclined loading.

3.1.7 In order to investigate a range of fill qualities, and native ground qualities, the constrained soil modulus was varied as follows:

M’ Values

Backfill Native Ground (kN/mz) (kN/mf)

33,000 1,000,000 rock

67,000 67,000 compact sand and gravel

200,000 20,000 loose sand-gravel or medium stiff clay

3.1.8 Probable bearing pressures were assessed for the arch footings, and foundation sizes derived accordingly.

21

3.1.9 Applying the design rules from the SMP/Glock 1979 method (Reference 9) to the structures in question, in conjunction with a normal quality of backfill (MO= 67,000W/m2), a maximum height of cover of 5.48m is feasible. For the same soil quality the SMP/Glock method predicts a buckling failure should occur at a height of cover of 12.lm. Using the ring compression theory, the ultimate seam strength capacity would be reached at a height of cover of 17.6m.

3.1.10 The study was carried out in planned stages. The results obtained from each stage allowed modification to be made to subsequent runs. Placement of backfill in compacted layers was simulated. The maximum heights of cover modelled in various stages were 5.48m, 12.lm and 17.6m respectively. In a final stage the effects of providing 1/2 span of selected backfill as opposed to 1 span of fill to either side of the structure, were investigated, together with the effects of providing a larger thrust beam and of removing the thrust beam. An investigation was also made into the effects of varying the footing sizes.

3.1.1 1 Since the primary purpose of the study was to observe if fundamental differences in behaviour occur between arches and ellipses, a simple elastic model was chosen for the backfill and native soil materials.

3.1.12 The pipe wall was modelled by CANDE as an elasto-plastic beam element. Metal properties assumed a yield stress of 220N/mm2 and a Young's Modulus (E) of 205kN/mm2. Beyond yield point strain hardening was assumed to occur with a modulus of 20.5W/mmZ. The pipe wall was approximated as a saw tooth profile to allow calculations of plastic moment capacity to be made by CANDE. For equilibrium to be achieved the pipe must carry the ring compression to which it is subjected. When plastic hinges begin to develop the moments developed at the hinges may not increase with increasing ring compression and plate curvature, since the overall moment carrying capacity of the pipe wall reduces with increasing axial load. Where plastic hinges start to form below thrust beam level additional movement and development of passive pressures can take place to maintain overall equilibrium.

In order to establish how re-entry angle might affect the behaviour of the arches additional runs were carried out for angles of 0" and 25".

3.2 Findings

3.2.1 Failure Modes .I

In order to try to simplify our findings they are reported under the headings of possible failure modes. In the initial stages comparison of results obtained using an angle of interface friction of 0" and 15" was carried out, which suggested the largest differences in ring compression between arches and ellipses occurred with an angle of friction of 0". All the results reported are based on an angle of friction of 0".

22

Headings:

Backfilling and Deflection Ring Compression Strain, Bending and Buckling Yielding Thrust Beam Connection and Size of Thrust Beam Extent of Fill Re-entry Angle Foundation Size

3.2.2 Backfrlling & Deflection

The ellipse profile deflects under its self weight by a considerably greater amount than the arch profile. Attempts to make the structures peak by simulating high compactive effort as the backfill is placed in layers (by means of a uniform surface live load), were not successful in terms of raising the crown up to or above the theoretical design position after placement of the fill above the crown. In practice ties are sometimes installed across the spring line to pull the structures back into shape, however, attempts to model this effect caused unduly high bending stresses and local distortions which made direct comparison of the behaviour of the arch and ellipse almost impossible.

For the purpose of this study it was therefore accepted that the elastic soil model-was not accurate in simulating the backfill process. In practice larger upward deflections counteracting the self weight deflections would be expected to take place.

Nevertheless backfilling of the arch with lower quality fill (M' = 33,000kN/m2):*did cause a recovery of the crown level for the arch profile before backfill reached crown level. The self weight deflection of the ellipse is so significant that the initial deflection of 116mm is only just within 2% of the maximum rise of the structure (1 26mm) advised by AASHTO as the acceptable limit during backfill and in service. If the geometry criteria was taken to be 2% of top rise the relative deflections between the spring line and the crown would exceed 63mm prior to commencement of backfilling above a height of cover of 2m.

The deflected profile of the arch is within tolerable limits until a height of cover of 1 lm is reached. Deflections increase at a significantly lesser rate with increasing fill height than those exhibited by the ellipse.

The horizontal deflections at the spring line are within 2% of half the structure span for all the heights of cover considered (up to 17.6m). As would be expected the horizontal deflections for the ellipse are greater than for the arch.

Bending stresses and total strains generated by self weight effects and by backfilling to crown level are consistently and significantly greater for ellipse profiles than for arch profiles. (Figures B-7 and B-8). By the stage that backfill reaches crown level peak strains experienced at any point in the arch and within the crown of the ellipse structure are not significantly in excess of 0.25m~ (milli-strain), which corresponds to

23

a steel stress of 55N/mm2. Strains in the arch crown are less than those in the ellipse crown. The bottom plates of the ellipse are however subjected to strains of up to 0.65ms over the same load stages, this corresponds to a stress of 133N/mm2. Strains for the crown plates are larger for the ellipse under self weight only, and tend to reduce slightly as the effect of the backfill counteracts the self weight.

From the table in Appendix C (Table C-2) it can be seen that horizontal spring line deflection predicted by the modified Iowa deflection equation (Reference 21) is consistently and significantly greater than the deflection predicted by the finite element study for either arches or ellipses. Ignoring self weight effects, which are very significant for ellipse profiles, the ellipse has deflections which are approximately double those of the arch.

Except for installations with unusually stiff backfills the horizontal deflections for ellipses are approximately 1/3 of those predicted by the modified Iowa equation (Reference 2 1 ) .

Reference to Table C-3 suggests that the vertical spring line deflections for the ellipse are consistently greater than for the arch, being in the order of 1.3 times greater on average. With reference to the maximum differential vertical deflection between the crown and the thrust beam position, which should give an indication of the amount of crown flattening and hence susceptibility to buckling instability, it is interesting to note that there is consistently less deflection (by a small margin of approximately 10%) for the arch structures.

At working load conditions there appears to be a fairly reasonable correlation between SMP/Glock predictions of crown deflection and the results from the FE analysis. For an M' of 67,000kN/m2 the finite element arch deflection is 0.9 times that predicted by SMP/Glock (1 9.5mm) and the finite element ellipse deflection is exactly equal to that predicted by SMP/Glock. The SMP/Glock method was referred to by Temporal and Johnson in their (Quy) load test report (Reference 24), and entails back calculation of the deflection at working load having obtained values of crown deflections, from Glock's work, occurring at buckling failure load. A linear relationship is assumed between load and log deflection.

It should be noted, however, that the FE results show a linear increase in deflection with load so the technique should be applied with caution for dead load conditions.

3.2.3 Ring Compression

The graphical results given for ring compression around the structure (Figures B-9 and B-10) show a dramatic change in ring compression occurring at the thrust beam position for both arches and ellipses.

The maximum ring compression always occurs below the thrust beam and is relatively insensitive to changes in backfill stiffness and native ground stiffness.

At a height of cover of 5.48m the ring compression in the ellipse profiles below the

24

thrust beam is less than the theoretical values obtained by either yHR,, or total overburden load W/2, of which the former is the greater. The maximum ring compression predicted by the FE analysis is approximately 75% of that predicted by yHR,. The ring compression in the arch profiles below the thrust beam is only just less than the theoretical value obtained by yHR, and is greater than the value given by W/2. The maximum ring compression in the ellipse is approximately 25% less than that in the arch.

The ring compression in the crown plates is apparently influenced to a greater degree by the stiffness of the backfill. Again the maximum ring compression in the ellipse tends to be somewhat lower than the ring compression in the arch, but by a smaller margin of approximately 15% for reasonably stiff fill material.

The phenomenon of the ring compression being greater for the side plates than the crown plate is obviously at variance with the model postulated by Glock in his Superspan publication (Reference 20). It appears that the thrust beams attract considerable vertical loading and encourage localised arching in the fill above the crown plates. This conclusion is supported by the reduction in free field earth pressure found to act on the crown for both arches and ellipses.

In Figures B-1 1 and B-12 the change in maximum ring compression, reported by the FE analysis, is enveloped for arches and ellipses, and for the crown and bottom plates.

Figure B-12 has been produced to highlight the disproportionately high ring compression which appears to be attracted by the arch profile, in particular, at low height of cover. "

For the ellipse, ring compression based on W/2 appears to be the most appropriate. At low covers of up to 2m the use of yHR, can significantly underestimate the amount of ring compression. As height of cover increases above 1.5m the W/2 prediction of maximum ring compression becomes more pessimistic compared to the FE results.

.a.*

The ellipse profile thrust beam appears to have a neutral effect up to a height of cover of lSm, after which point the thrust beam attracts loading which is transferred into the bottom plates of the structure.

The arch structure attracts greater ring compression loading than the ellipse at all heights of cover. At a height of cover of 1.3m, according to the FE analysis, the arch attracts significantly more loading than is predicted by either W/2 or yHR,. A more realistic prediction of ring compression is given by the relationship:

Ring compression = [ 1 + 0.35 (S-H) ] or yHR,, 2 S

whichever is the greater.

At heights of cover of 5.48m and 12.lm where the Glock method predicts the occurrence of buckling in the crown plates, the thrust in the bottom plates is overestimated by Glock, as compared to the FE method. Due to the fact that Glock

25

does not attempt to model localised soil arching above the crown plates, and that he applies the full crown overburden pressure to a flattened crown plate, the values of ring compression predicted by Glock in the crown plates and the bottom plates are significantly greater than those predicted by FE analysis.

3.2.4 Strain, Bending and Buckling

Strains: For the model adopted outer fibre yielding of the pipe wall occurs at a strain in the order of 1 .07m~. No strains significantly in excess of 1.07m~ are reported for any part of the arch or ellipse for any of fill materials modelled, up to working load conditions at height of cover of 5.48m.

For increases in height of cover above 5.48m compressive strains in the crown plates tend to continue to increase in a predominantly linear fashion and the reported values are remarkably similar for the arch and ellipse profile crowns (Figures B-8, B-13 and B-14). At a height of cover of 17.6m maximum reported strains are approaching or are just over yield.

Milli-strain (mc) at 17.6m cover in crown plates

M' Arch Ellipse (kN/m2) (mc)

33,000 1.1 1.1

67,000 0.9 1.2

200,000 0.7 0.65

Tensile strains in the crown plates (signifying bending effects) are generally similar for both arch and ellipse profile and are generally less than 0.30m~. As height of cover increases these strains diminish and become negligible.

As already noted, strains in the ellipse profile side and bottom plates tend to be disproportionately greater than for the arch profile for heights of cover up to maximum working load conditions at 5.48m. The cause is thought to be primarily due to two localised areas of support representing "hard spots" beneath the bottom plates where bending is induced when the self weight of the ellipse is released.

Thus ellipse structures appear to exhibit larger strains up to maximum working load conditions at 5.48m. strain in the side plates reported for the model with M' = 33,000kN/m2 increases dramatically for the arch in the side plates. This tendency is lessened with better quality backfills.

At heights of cover between 5.48m and 12.lm the maximum .-

Figures B- 1 6 and B- 1 8 illustrate the typical distribution of strain around the ellipse and arch profiles.

26

3.2.5

3.2.6

Bending: The FE analysis indicates that bending moments developed in the structure wall, inclusive of self weight effects, are consistently higher for the ellipse than the arch profiles up to a height of cover of 5.48m (Figure B-7). Above this height maximum hogging moments (deflection into the fill) are very similar, for the arch and ellipse profiles. Sagging moments (which could trigger an inward buckle) are substantially less for arch than the ellipse profiles. Positions of peak bending stresses tend to fluctuate without any discernible pattern.

Figures B- 15 and B- 17 illustrate the typical distribution of bending moments around the ellipse and arch profiles.

Buckling: In table C-4 the critical ring compressions and critical normal pressures corresponding to predictions of buckling failure are summarised for range of the generally recognised buckling theories. Predictions to Meyerhof and Baikie (Reference 3) incorporating their empirical modification to ensure predicted values of buckling stress are always less than yield, consistently give substantially lower predictions for critical pressure and ring compression than all the other theories, except for Glock for poor fills with a constrained modulus of 33,000kN/m2.

The predictions given by the SMP/Glock (Reference 9) buckling calculation are consistently less than those given by Cheney 1963 (Reference 32), Meyerhof and Baikie (Reference 3) without empirical modification, Forrestal and H e m a n 1965 (Reference 33), Luscher 1966 (Reference 34), Dunns and Butterfield 197 1 (Reference 3 9 , Cheney 1976 (Reference 37) and Chelpati and Allgood (Reference 36) as adopted by CANDE. All the above buckling theories show critical ring compression and critical soil pressure increasing as a function of increasing constrained soil modulus. Only SMP/Glock at M' = 33,000kN/m2 predicts a buckling stress less than yield stress for the MP200, 7mm plates under investigation. Use of a constrained soil modulus of 40,000kN/mz or more should ensure complete yielding due to axial load becomes more critical than buckling.

Yielding

The FE analysis shows that under extreme loadings very large strains can develop in the lower part of the structure without the formation of a failure mechanism.

Thrust Beam Connection and Size of Thrust Beam

It appears that the shear force developed at the thrust beam connection acts (at all but low spans for ellipse structures) in the opposite direction to that predicted by the Glock model. An assessment of the maximum shear force predicted by the FE analysis at the thrust beam connection has been carried out and found to lie within an envelope of maximum ring compression, (as proposed and re-defined in Section 3.2.3) multiplied by 0.4, for both arches and ellipses, with a standard thrust beam with a height of vertical face equal to RT x 0.12.

Thrust beams of the size modelled by Glock with vertical face sizes equal to RT x 0.19

27

appear to attract a significantly greater mount of shear at the thrust beam connection. Whilst crown pressure and crown ring compression reduce somewhat, the ring compression in the bottom plates increases suggesting that additional loading is attracted to the structure.

Figures B-9 and B-10 show this trend, and also show that omission of the thrust beams altogether would result in significantly higher ring compression being generated in the crown plates. This constitutes an increase in ring compression in the area most vulnerable to a buckling type failure. Whilst the arch would still would attract more ring compression than the ellipse, both structures would carry substantially less ring compression than that calculated by yHRT.

,

Ground Level //AY// //AY//

Additional load from side f i l l arching over crown

Loading from soil

-r SECTION THROUGH ELLIPSE PROFILE

\ Resultant Load

Resultant Thrust from Earth Pressure developed

Pressure from Structure Wall

Resultant Shear on Thrust Beam Connection

DETAIL AT THRUST BEAM

n

Figure 6 - Forces developed on thrust bems

28

Omission of the thrust beam substantially increases the bending stresses generated at the thrust beam position. This effect, coupled with the increased thrust developed in the crown plates suggests that omission of the thrust beam is not a recommended procedure.

Provision of standard size thrust beams, as opposed to the large thrust beams assumed by Glock, gives similar benefits to the crown plates, but should not cause a problem with the provision of a satisfactory thrust beam connection.

Analysis of the forces acting at the thrust beam connection suggest that the tangential shear generated by the vertical load on the top of the thrust beam is usually slightly greater than the opposing tangential shear generated by horizontal earth pressures on the side face of the thrust beam. Much of the out of balance shear force at the thrust beam connection appears to be generated by interface friction developed at the top face of the thrust beam, as shown in Figure 6.

3.2.7 Extent of Fill

The effects, in the study, of replacing the selected fill outside the limit of s p d 2 either side of the arch and ellipse with lower quality general fill with an M' = 5,000kN/m2 are negligible for the arch structure in terms of deflection and ring compression. A slight increase (10%) in bending stress is observed, which is not considered significant.

The ellipse profile attracts approximately 13% extra ring compression, the deflections and bending stresses increase by a similar percentage. The effects for the ellipse, though greater than for the arch, are not thought to be very onerous. Given the cost savings likely to be obtained by reducing the extent of the selected side fill it would be economical to increase the factor of safety required for ring compression by 15% for ellipses, and to allow a minimum extent of selected side fill of span/2.

3.2.8 Re-entry Angle

Re-entry angles of 0", 10" and 25" were to be modelled. However, due to geometrical approximations which had to be made, the final beam elements were actually inclined at angles of -8.6", 5" and 21" to the vertical at the top of the footings. The results we have obtained suggest that maximum ring compression decreases with increasing re-entry angle, and that the arch behaviour starts to become more similar to that of the ellipse. The variation in ring compression between a re-entry angle of Oo and 10" is minimal.

The most significant finding is that in the case of the model with a 0" re-entry angle, the restraining influence of the base appears to prevent free outward movement of the pipe wall. Additionally there is a tendency for the curvature of the pipe wall to straighten and flatten with increasing load. A substantial bending moment also develops. A potential for the pipe wall to be subjected to high compressive loadings in conjunction, ultimately, with the formation of a reversed curvature of the wall is observed. In such an instance the Euler type buckling failure referred to in the AISI books (Reference 11 and 16) become a serious consideration.

29

Maximum strains are substantially greater for the 0" re-entry angle than the others considered. The above findings may be slightly onerous due to the approximations made in the model. However, we conclude that arches with a zero re-entry angle should not be permitted as a standard installation, and that the normal range should be limited to between 10" and 25".

3.2.9 Foundation Size

An analysis was carried out using three footing sizes for the model with a constrained soil modulus of 67,000kN/m2. The control size of foundation was 2m wide, and alternatives lm wide and 5m wide were substituted in turn to investigate the possible effects of undersizing and oversizing the foundation.

As might be expected, the vertical deflections increase for the smaller foundation and decrease for the larger foundation, but only by a very small percentage (approximately 7.5%). Ring compression is basically unchanged varying by only 4% between the control value and the largest ring compression associated with the widest foundation, and the smallest ring compression associated with the narrowest foundation. Other effects on the metal plate are also very small. Irrespective of foundation size, the footings always tend to move sideways away from the centre of the arch and toward the fill.

The main FE runs incorporated footing sizes matched to native soils stiffness. Reported values of bearing pressure at working height of cover on the initially designed and sized foundations for native soil with M' = 33,000kN/m2, 67,000kNlm2 and 1,000,000kN/m2 were generally in the order of 25% higher than predicted by the design calculation. Interpretation of the results becomes somewhat difficult, however, for the largest footing, with higher bearing pressures generally being experienced at the outside edge of the footing within the side fill. It appears that the footings attract a higher loading from the metal plate than was assumed in the initial sizing calculation, but that a much reduced vertical soil pressure on the horizontal surface of the footing means there was less total load on the footing, according to the FE results, than had been originally allowed for.

As previously noted in 3.2.8, some inaccuracies are inherent in the model since the final beam element loading the base makes a lesser inclined angle to the vertical than the re-entry angle it was intended to represent. This may account for the increased bearing pressure observed.

The ring compression in the bottom plates was found to be greater than the value of W/2 used in the foundation design by 13% for a re-entry angle of 10". Ring compressions calculated using yHR, would give an over-estimate against that found in the FE analysis by approximately 6%.

Variation in foundation size appears to have no significant effect upon the behaviour of the corrugated steel, and it could be argued that to ensure safe foundation design the value of ring compression for the calculation of foundation size should be based on the modified values proposed in Section 3.2.3 as the greater of:

30

- W [ 1 + 0.35 6 - H ) ] or yHR, 2 S

i

CO-existent overburden (free field) pressure could be taken to act at the top svrface of the foundation, and active pressure at the rear vertical surface. This may, however, result in a somewhat conservative design and it is suggested that some trial calculations be carried out to establish the effect of such a design rule upon foundation size before it is finally adopted.

The allowable bearing pressures for strip footings predicted by Terzaghi in conjunction with a factor of safety of 3 should be used to size foundations at working load condition (Reference 23).

At the ultimate limit state it is suggested that the maximum ring compression in the bottom plates be taken as that predicted by Glock, coincidental with the occurrence of significant movement and a buckling type failure of the crown plates. Pressures acting on the base should be taken as nominal working values, and the ultimate induced bearing pressures should be checked against those predicted using the Meyerhof method for footings subjected to inclined loadings (Reference 23).

4.0 REVIEW OF TECHNICAL LITERATURE

4.1 The review of the technical literature listed in Section 6 covers a vast amount of work and information which has been collated over the years. Often this information appears to be contradictory or inconsistent.

4.2 Since there have been a substantial number of long span structures actually constructed (there were 600 recorded in the Federal Highway Administration Report ‘Review of the Design and Construction of Long-Span Corrugated Metal, Buried Culverts’, Reference 22) the reports and investigations into failures are of great importance and significance. Of the twenty failures referred to in the review literature and articles none appear to be attributable to long span structures incorporating thrust beams, which have been put into service. The failures usually occurred during construction. The reasons for failures are not always fully reported due to the litigation which resulted, but there appears to be a general consensus that the following factors or combination of factors are usually critical:

0 backfill incorporating frozen material

0 poor quality non granular backfill

0 limited extent of backfill (1.86m from side plates)

0 absence of thrust beams

0 use of special features other than thrust beams

31

poor workmanship in terms of controlling profile shapes, consistency of backfill, adequacy of backfill and compaction

permitting premature loading of the installation by construction plant at low heights of cover.

0 use of excessively squat structures with high span to rise ratios

0 failure to appreciate hydraulic load effects of flowing water during and after construction.

4.3 Where failures have occurred during the construction of long span structures with thrust beams the causes have been attributable to poor construction practice on site in terms of uneven placing of fill, use of frozen backfill, or poor control of structure geometry.

4.4 One of the most dramatic failures reported is the structure on the Paulding County Route 180 near Antwerp, Ohio where a catastrophic failure occurred killing and seriously injuring road users. This occurred after the structure had been in service for 10 years. In this instance thrust beams were not installed, but the primary cause was attributed to the use of unsuitable backfill. Pavement deflections of 5 to 6 inches and "some flattening of the curvature of the arch" were observed in the structure's first year in service (1 973/74). Flattening of the crown near the sides and peaking of the centre was observed in 1976 and periodic evaluations were recommended. The structure failed in 1983.

4.5 Full. scale field monitoring of long span structures for both arches and ellipses has been carried out. Most of the structures monitored have low heights of cover of approximately span/lO, but there are also some notable high cover installations.

4.6 Model testing in the laboratory and finite element analysis and studies are also reviewed. In some instances FE analyses have been used in an attempt to model the behaviour of an installation which has been installed and monitored (References 1,2,5,7 and 8).

4.7 A summary of the principal structure types reviewed is given in tables C-5(i), C-5 (ii) and C-5 (iii) in Appendix C.

4.8 There appears to be a general agreement in the literature reviewed on the following points:

3

1. It is very difficult to predict or to attempt to design for bending stresses in buried flexible structures. Attempts to use FE methods have necessitated the use of complex soil and compaction models to back analyse and match effects observed in practice even under backfilling and dead load conditions. Use of FE to predict live load effects have not been generally successful under low cover conditions.

32

.. 11. The benefits of using thrust beams and their effects in shedding or attracting

loading are difficult to define. In practical terms the thrust beam appears to be a very satisfactory construction aid in terms of stabilising the crown whilst the first fill is placed and tracked over the crown plates. Once in service the neutral effect shown in our FE analysis for ellipses under shallow fill seems to be consistent with some of the field tests. Generally however, for arches and ellipses under higher fills (above span/lO) field measurement usually show that a change in shear occurs at the thrust beam and that ring compression in the top plates is less than ring compression in the bottom plates. This effect has also been predicted by other FE studies.

... 111. FE studies tend to indicate that maximum ring compression due to dead load

is a function primarily of structure geometry rather than soil stiffness or foundation size.

iv. Time dependent effects can be very significant in terms of increasing deflection and ring compression. Reported values of ring compressions on monitored structures, which were initially less than values calculated using W/2 or yHR,, became substantially greater with time.

v. At low covers (in the order of span/lO) measured values of ring compression for both arch and ellipse profiles are greater than the largest values predicted by W/2 or yHR,. In the case of ellipse profiles these measurements have.been taken for structures without thrust beams.

c

5.0 CONCLUSIONS AND RECOMMENDATIONS

5.1 From the foregoing review of design methods, of the FE study carried out by ourselves, and of the wealth of technical papers and field tests carried out, our principal conclusion must be that there is much conflicting information concerning the behaviour and design approaches for buried metal corrugated steel structures, particularly with respect to long span structures.

5.2 This state of affairs is probably due, in the main, to the complexity of the soil-steel interaction problem. Problems in modelling and prediction of behaviour stem from the need to take into account the stress and deflection history of the metal wall, of the native ground and of the fill material during all stages of construction including compaction of the backfill. The elasto-plastic behaviour of the metal wall can be modelled fairly easily, however modelling the inelastic behaviour of the native ground and the fill material presents much more of a problem. Other contributory factors making a unified approach difficult are the variations of available arch and ellipse geometries, variation in interface friction between the fill and all parts of the structure including the thrust beam and the foundations. Further, it is well documented that time dependent effects occur which tend to increase dead load effects upon the structures. To date, finite element analysis appears to have modelled the problem in the most satisfactory manner.

33

5.3

5.4

5.5

5.6

The Glock model for large span ellipses with thrust beams causes the thrust beams to shed ring compression developed in the crown plates into the side fill. This effect does not appear to have been observed or confirmed by either field measurement or FE techniques. Some field measurements suggest that the thrust beam has a neutral effect, whilst others confirm the FE model findings where substantial loading is transmitted onto and carried by the thrust beams inducing higher ring compression into the bottom plates.

Any design approach adopted should arguably try to cover all the possible behaviour and failure modes which could develop for a wide range of arch and ellipse installations, in conjunction with the use of factors of safety which reflect the level of uncertainty present in the short and long term methods of estimating the load induced effects.

Despite the above comments, confidence should be drawn from the significant number of long span structures which have been successfully installed with thrust beams. Having studied the design rules used for these structures, application of the following simple empirical rules would appear to be all that should be necessary:

1.

.. 11.

... 111.

iv.

V.

vi .

vii.

Metal plate thickness and seam strength capacity should be adequate to carry ring compression calculated on the basis of dead load and live load overburden pressure times top radius, with a factor of safety of 3 applied to seam strength and of 2 applied to yield stress.

Avoid buckling failures by the use of good quality backfill defined by soil classification based on grading limits. The backfill should be well compacted to 90% density to BS1377: 1990: Part 4: Clause 3.7 (Reference 39).

Limit the maximum top radius which can be used, or the maximum span.

Place geometry limits on the maximum and minimum ratio of top radius to side radius permitted.

Use manufacturer’s recommendations so that the corrugated plates are adequate to withstand installation loadings including backfilling.

Carefully control the shape of the structure during backfilling as well as the placement and compaction of suitable fill.

Limit the minimum height of cover to avoid failure due to concentrated live loading causing a localised soil movement and inward buckle.

“i

Full scale load testing of long span structures carried out in this country to investigate the effects of live loading show that only the portion of the structure above the spring line position responds to the applied loading in terms of deflection, ring compression and strain in the metal plates. These tests have been carried out at shallow heights’ of cover.

34

5.7

5 .8

5.9

Ring compression generated by dead load only would appear to be higher for arch structures at low heights of cover than that predicted using yHRT and W/2. From the findings of our FE study we recommend that more accurate predictions of maximum ring compression will be given by the greater of the following equations:

- W [ 1 + 0.35 (S-H)] or yHR, 2 S

The expression yHRT can give larger values of ring compression at high cover conditions.

For the ellipse structure modelled in the FE study maximum ring compression does not appear to exceed W/2 at any height of cover. Results from field tests, however, suggest that installed ellipses which have been monitored can attract, in the long term, loads in excess of these values, but that arches do not attract a disproportionately greater amount of ring compression. We therefore recommend that the same enhanced values for maximum ring compression due to dead load be adopted for ellipses in conjunction with a relaxation for the minimum extent of selected side fill from span to s p d 2 or top rise x 413.

At low heights of cover the DOT HB live loading (Reference 14 and 25) theoretically generates significantly more ring compression than the dead load effects, but structures installed to date have probably not been under-designed since the method of calculating live load effects is somewhat conservative and fails to take full account of the load distribution properties of the road pavement.

5.10 With regard to buckling, it is considered that the model postulated by Glock is possibly inaccurate but conservative in the following respects:

1.

I .. Full free field overburden pressure is carried by the crown. No local arching over the crown is taken into account, which is a phenomenon found in the finite element study, and is measured in most of the structures which have been monitored. Thus the ring compression above the thrust beams predicted by the Glock model is always greater than the ring compression predicted by the FE study.

.. 11. Maximum ring compression in the bottom plates due to dead load effects is

also over estimated by the Glock method in comparison with results from the FE study. The Glock method represents a possible (ultimate limit state) failure mechanism. The method fails to take account of soil arching over the crown onto the thrust beams. This results in a prediction of shear in the thrust beam connection acting in the opposite direction to that indicated by the FE analysis. If a slip membrane were to be introduced on the top surface of the thrust beam, which is something that could occur in practice if any attempt is made to waterproof the structure, the local arching phenomenon observed in the FE study and in practice could be substantially reduced.

35

iii. There is a correlation between the Glock buckling predictions and previously established practice in that for the largest spans using corrugations with a 200- wavelength and a 51mm amplitude, yield stress rather than buckling becomes the critical factor providing soil with a constrained soil modulus of at least 40,000kN/m2 is used for selected backfill.

5.1 1 Our recommendations for a design method for large span structures incorporating thrust beams for both arches and ellipses are as follows:

a) LIMITATIONS AND EMPIRICAL REQUIREMENTS

1. Maximum span 13.7m

.. 11. Maximum top radius RT given by E1 2 0.000025

M'R;

iii. For the ratio of top radiuslside radius limiting values of between 2 and 4 should be adopted. The crown aperture should be 80". Bottom radius must be the same as top radius.

iv. Good quality non plastic soil should be used for backfill with an M' value of not less than 40,000kN/m2 compacted to 90% density to BS1377: 1990: Part 4: Clause 3.7 (Reference 39).

v. The minimum extent of the selected fill should be the greater of span/2 or top rise x 413.

vi. Re-entry angles for arches should not exceed the limits of 10" to 25".

vii. Where poor ground conditions exist the foundations for arch profile structures must be such that the side fill will not settle to a greater degree than the structure. Piled foundations would not therefore usually be suitable.

viii. Backfill to be tested by plate load testing during construction.

ix. Geometry limits of k 2 % for span and rise should not be exceeded as a variation fiom the theoretical profile at any stage. For arches the rise should be taken as the distance from top of footing to top of crown.

X. Thrust beam size should be to manufacturer's recommendations with a vertical face size approximately equal to 0. 12RT

xi. A minimum height of cover of 1.5m should be observed for all structures subjected to HB loading.

36

b) DESIGN REQUIREMENTS

1. For buckling and a check of seam strength capacity at ultimate limit state (collapse) conditions the original SMP/Glock proposals appear to be satisfactory with crown pressures calculated in exactly the same manner. No extrapolation of the design charts should be permitted for normal installations.

.. 11. Deflection at working load conditions should be within the limits of k 2%

from the design profile. Working load deflection of the crown plates relative to the thrust beams may be estimated from when the first layer of fill has been placed over the structure, using the Glock graph for deflection at failure, and assuming a linear relationship between load and log deflection.

iii. A check for the thrust beam connection should be carried out using the Glock graph for shear. A further check should be made at working load conditions based on a shear force equal to maximum ring compression multiplied by 0.4.

iv. At working load conditions maximum dead load ring compression shall be taken as the greater of [W/2][1+0.3S(S-H)/S] or yHR,, acting in the bottom plates. Coincidental live load ring compression should be based on the nominal live load crown pressure derived by applying the DOT rules for loading and load dispersal in BD12/88 (Reference 14). A factor of safety of 3 should be applied to ultimate ring compression and a factor of safety of 2 should be applied to yield stress.

v. For arches the tangential ring compression which should be assumed to act upon the foundations at working load conditions should be the greater of [W/2][ 1+0.35(S-H)/S] or yHRT. The co-existent earth pressure acting vertically on the top of the base should be equal to the free field pressure, and the horizontal earth pressure on the vertical face of the footing shall be taken as the active earth pressure. A factor of safety of 3 should be applied to the ultimate load carrying capacity of the footing calculated in accordance with the standard method by Terzaghi (Reference 23). Further, the tangential ring compression at ultimate (collapse) load conditions should be taken to be equal to the ring compression given by the Glock graphs for the bottom plates of the structure, applied simultaneously with the same nominal and horizontal and vertical pressures assumed to act upon the base at working load conditions. The resulting bearing pressures should not exceed the ultimate bearing pressure predicted by Meyerhof (Reference 23) for footings subjected to inclined loadings.

vi. It is recommended that in addition to the above the requirements for fill selection and measures to ensure durability comply fully with BD12/88 (Reference 14).

5.12 Finally it is recommended that simple field monitoring of deflection and ring compression be undertaken to try to verify and hopefully refine the suggested design rules as new structures are installed on DOT projects. It should be remembered that

37

application of the design rules recommended in this report will effectively result in a more conservative design of long span arches and ellipses than has hitherto been the case due to the enhanced dead loading effects which are incorporated. If these changes represent a better estimate of the loading attracted by arches and ellipses it would be logical to allow a reduction in the factor of safety required for seam strength, particularly at lower covers where the method of estimating ring compression under live loading may also be rather conservative. At the same time, however, it is believed that greater economies can be achieved by reducing the required extent of backfill but accepting, at least for the time being, the more conservative requirements for designing the pipe wall and in the case of arches, the footings.

6 ACKNOWLEDGEMENTS

The authors would like to acknowledge the assistance received from Dr M P O'Reilly, Dr J Temporal and Mr D G Boden from the Bridges and Ground Engineering Resource Centre at TRL, and from members of the Bridges Engineering Division at the Highways Agency of the Department of Transport.

7

7. I

1.

3 'a

3.

4.

5 .

6 .

7.

REFERENCES AND OTHER REVIEW LITERATURE

References

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Chand C S, Espinoya J M and Selig E T (1980). Computer analysis of Newton Creek culvert. JASCE Geotech Eng, volume 106, No GT5, page 531 - 556.

Meyerhof G G and Baikie L D (1970). Some research on underground flexible arches. Nova Scotia Technical College, Canada. Paper submitted to International Road Federation Conference, Montreal, May 1970.

Meyerhof G G and Fisher C L (1963). Composite design of underground steel structures. The Engineering Journal, page 36, EIC-63-GEOTECH, 5 September 1963.

Seed R B and Chang Yu Ou (1986). Measurement and analyses of compaction effects on a long-span culvert. Stanford University, Stanford, CA94305, USA.

Meyerhof G G (1968). Problems in the design of shallow-buried steel structures. Proceedings of Canadian Structural Engineering Conference, Toronto, 1968, pp 55-63.

Leonards G A, Juang Wu and Stetkar (1985). Predicting performance of buried metal conduits. Transportation Research Record 1008, Culverts: Analysis of Soil-Culvert Interaction and Design, Transportation Research Board National Research Council.

38

8.

9.

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13.

14.

15.

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20.

21.

Seed R B and Duncan J M (1 986). Compaction-induced stresses and deformations for yielding structures. The Journal of the Geotechnical Engineering Division, ASCE, Vol 112, No.1 January 1986.

Stirling Maynard and Partners (1979). structures. Unpublished report to Armco Ltd.

Design of h c o multi-plate superspan

Stirling Maynard and Partners (1984). The design of Armco multi-plate superspan structures with worked examples. Unpublished report to Armco Ltd, August 1984.

American Iron and Steel Institute (1984). Handbook of steel drainage and highway construction products. First Canadian Edition First Printing, AISI, Washington DC.

The American Association of State Highway and Transportation Officials (1 969). Standard specification for highway bridges. AASHTO, Washington DC.

The American Association of State Highway and Transportation Officials. ( 1977). Standard specifications for highway bridges. Twelfth Edition (with 1978 amendments), AASHTO, Washington DC.

BD12/82. Corrugated steel buried structures. Design Manual for Roads and Bridges (DMRB 2.2.1), DOT.

Abdel-Sayed G A and Bakht B (1981). Soil-steel structure design by the Ontario Code: Part 2, structural considerations. Canadian Journal of Civil Engineering. Volume 8, Number 3, September 1981, pp 331-341.

American Iron and Steel Institute (1971). Handbook of steel drainage and highway construction products. Second Edition 1971, AISI, Washington DC..

Ontario Highway Bridge Code. Soil steel structures and section C12, commentary. published by the Ministry of Transportation and Communications, Ontario, 1983.

Kloppel K and Glock D (1970). Theoretische und experimentelle underschungen zu den tranglastroblemen biegewiecher, in die erde eingebetteter rohre. Publication No. 10, Veroffentlichung des Institutes f%r Statik und Stahlbau, T.H. Darmstadt, Germany.

Kloppel K and Glock D (1974). The dimensioning of embedded flexible pipes of the Armco multi-plate type. Unpublished report to Armco Ltd.

Glock D (1973). Superspan. Unpublished report to Armco, T.H. D m s t a d t , Germany.

Stirling Maynard and Partners (1 986). Armco superspan design proposals, supplementary information. Requested by the Department of Transport.

. ..

. I

39

22.

23.

24.

25.

26.

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31.

32.

33.

34.

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36.

Selig E T, Abel J F, Kulhawy F H and Falby W E (1977). Review of the design and construction of long-span, corrugated metal, buried culverts. FHWA/RD-77-13 1, Federal Highway Administration, Washington D C.

Lambe T W and Whitman R V (1969). Soil Mechanics. Wiley, New York.

Temporal J and Johnson P E (1 988). Loading test on two long span corrugated steel culverts. DTp, TRRL Report RR141.

BD37/88. Loads for highway bridges. Design Manual for Roads and Bridges (DMRB 1.3), DOT.

Structural evaluation of new concepts for long-span culverts and culvert installations. FHWA-RD- 1 15, Federal Highway Administration, Washington DC, December 1979.

Katona, Smith, Odello and Allgood (1976). CANDE - a modem approach for the structural design and analysis of buried culverts. Federal Highway Administration, Washington D.C. Final Report No. FHWA-RD-77-5, October 1976.

Thorburn and Partners (1 982). Loading on buried highway structures. Final report to the Department of Transport, Bridges Engineering Standards Division, May 1982.

Spangler M G (1941), The structural design of flexible pipe culverts. Bulletin No. 153, Engineering Experimental Station, Iowa State College.

Marston A (1930). The theory of external loads on closed conduits in the light of the latest experiments. Proc. HRB, Vol 9, 1930, pp 138-170.

White H L and Layer, L P (1960). Corrugated metal conduit as a compression ring. Proc HRB, Vol 39, 1960, pp 389-397.

Cheney J A (1 963). Bending and buckling of thin-walled, open section rings. Journal of Engineering Mechanics Division ASCE, Vol 89, EM5.

Forrestal M J and Hermann G (1965). Buckling of a long cylindrical shell surrounded by an elastic medium. Inst. J. Solid Structures, Vol I, pp 297-309, Pergamon Press Ltd.

Luscher U (1966). Buckling of soil-surrounded tubes. Proc. ASCE, Journal of Soil Mechanics and Foundation Division, Vo192, SM6, pp 211 - 228, November 1966.

Dunns C S and Butterfield R (1971). Flexible buried cylinders, Part I11 - buckling behaviour. 1nt.J Rock Mech. Min. Sc., Vol 8, pp 613-627, Pergamon Press.

Chelapati C V and Allgood J R (1972). Medium. HRB, No.413, pp 77-88.

Buckling of Cylinders in a Confining

40

37. Cheney J A (1976). Buckling of thin-walled cylindrical shells in soil. DOE, DTp, TRRL SR204.

38. Watkins R K (1966). Structural design of buried circular conduits. Highway Research Record No. 145, pp 1-16.

39. British Standards Institution (1990). BS 1377:Part 4: 1990: Soils for civil engineering purposes - compaction-related tests.

7.2 Review Literature

1. Selig E I and S J Calabrese (1975). Performance of a large corrugated steel culvert. Transportation Research Record 548, pp 62-76.

2. Lefebre G, Laliberte M, Lefebre L, Lafleur I and Fisher C (1975). Measurement of soil arching above a large diameter flexible culvert. Canadian Geotech Journal, vol 13, pp 58-71.

3. Bakht B (1981). Soil steel structure response to live loads. JASCE Geotech Eng Volume 107, No GT6, pp 779-798.

4. Beal D B (1982). Field tests on a long span aluminium culvert. JASCE Geotech Eng Volume 108, No GT6, p 873-890.

5 . McVay M C and Selig E T (1 982). Performance and analysis of a long-span culvert. Transportation Research Record 878, pp 23-29.

6. Kay J K and Flint R C L (1982). corrugated metal and soil. Transportation Research Record 878, pp 34-37.

Heavy vehicle loading of arch structure of

7. Bakht B (1985). Live load response of a soil steel structure with a relieving slab. Transportation Research Record 1008, pp 1-7.

8. Selig E T and Musser S C (1 985). Performance evaluation of a rib-reinforced culvert. Transportation Research Record 1008, pp 1 1 7- 122.

9. Moore I D (1 989). Elastic buckling of buried flexible tubes - a review of theory and experiment. Journal of Geotechnical Engineering, Vol 115, No.3, pp 55-63.

10. Moore I D (1988). Elastic stability of buried elliptical tubes. Technical Note, Geotechnique 38, No.4, page 613-618.

1 1. MCVay M C (1986). Long-term behaviour of buried large-span culverts. Journal of Geotechnical Engineering, Vol 1 12, No.4, pp 424-443.

12. Spangler M G. Second Edition, International Textbook Company, Scrunton, Pennsylvania.

Soils engineering supporting strength of underground conduits.

41

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

Crabb G I and Carder D R (1985). Loading test on buried flexible pipes to validate a new design model. DTp, TRRL Report RR28.

Dickin E A and Leung C F (1 983). Centrifugal model tests on vertical anchor plates. Journal of Geotechnical Engineering, Vol 109, No. 12, pp 1503-1525.

Harrison J A (1 987). Correlation between California bearing ratio and dynamic cone penetrometer strength measurement of soils. Technical Note 463, Ground Engineering Group, Proc.Inst. Civ. Engrs, Part 2.

Ghobrial and Abdel-Sayed ( 1985). Inelastic buckling of soil-steel structures. Transportation Research Record 1008, pp 7- 14. J

Katona and Adel Y Akl (1985). slotted joints. Transportation Research Record 1008, pp 22-32.

Analysis and behaviour of buried culverts with

Selig E T. Instrumentation of large buried culverts. Performance Monitoring for Geotechnical Construction, pp 159-1 8 1, ASTM STP 584, American Society For Testing and Materials.

Engineering Services Laboratory (1 985). Testing on granular backfill to corrugated steel buried structure - A45 Cambridge Northern bypass near Quy Mill. Report to Transport and Road Research Laboratory, Crowthorne.

Nielson, Bhandhausavee, Yeb (1 969). Determination of modulus of soil reaction from standard soil tests. Highway Research Board Record No. 284, HRB, Washington DC, pp 1-12.

Burland J B (1969). Reply to discussions procedures. Conference on In-Situ Investigations in Soils and Rocks. British Geotechnical Society.

Pocock, Lawrence, Taylor (1 980). Behaviour of a shallow buried pipeline under static and rolling wheel loads. TRRL Report LR954.

Wilson (1990). The Nova span bridge system. Engineers, Structural Engineering Conference, Adelaide, October 1990.

The Australian Institution of

Johnson P E, Temporal J and Watts G R A (1989). The effect of pavement layers on the behaviour of corrugated steel culverts. DTp, TRRL Report RR209.

Highway Research Report (1 968). Seam strength of asphalt coated structural plate pipe. Materials and Research Department, Research Report No. MR636407, Transportation Agency, Department of Public Works, Division of Highways, California.

Mina C and Bakht B (1981). Soil-steel structure design by the Ontario code: Part 1. General and geotechnical considerations. Canadian Journal of Civil Engineering, Volume 8, Number 3, September 1981, page 317.

42

27.

28.

29.

30.

31.

32.

33.

34.

Compston, Cray, Schofield, and Sham (1978). Design and construction of buried thin-wall pipes. CIRIA Report 78.

Allgood J R (1970). Structures in soils under high loads. ASCE National Structural Engineering Meeting, Portland, Oregon, USA.

Temporal J, Barratt D A and Hunnibell (1985). Loading tests on an Armco pipe. DTp, TRFU Report RR32.

Structural evaluation of new concepts for long-span culverts and culvert installations. Report No FHWA/RD/79/115, Federal Highway Administration, Washington DC, (1979).

Gumbel J E (1 983). Analysis and design of buried flexible pipes. Thesis submitted to University of Surrey, 1983.

Vaslestad J (1 989). Long-term behaviour of flexible long-span culverts. Norwegian Road Research Laboratory, English Translation.

Construction considerations and control for soil-steel bridge structures. Journal of Civil Engineering, Volume 8, Number 4, December 1981, Page 519:.

Stirling Maynard and Partners, Notes for the determination of modulus of soil. reaction 'E' for h c o structures.

Canadian

".

43

A P P E N D I X A

APPENDIX A

List of Figures in Text Page

Figure 1 Semi-circular Arch Figure 2 Figure 3 Figure 4 Figure 5 Glock Superspan Model Figure 6

Demarcation of Two Buckling Zones Active and Passive Soil Pressure Zones Structural Mode1 of Pipe Arch

Forces Developed on Thrust Beams

4 9

10 11 13 28

List of Figures in Appendix B

Figure B-1 Figure B-2 Figure B-3 Figure B-4 Figure B-5 Figure B-6 Figure B-7 Figure B-8 Figure B-9 Figure B-10 Figure B-1 1 Figure B-12, Figure B-13 Figure B-14 Figure B-15

Figure B-16

Figure B-17

Figure B-I8

Comparison Between SMPIGlock and AASHTO, Ht cover 1 Sm, Ellipse Profile A Comparison Between SMP/Glock and AASHTO, Ht cover 1 Sm, Ellipse Profile B Comparison Between SMP/Glock and AASHTO, Dead Loads, Ellipse Profile A Comparison Between SMP/Glock and AASHTO, Dead Loads, Ellipse Profile B FE mesh for arch FE mesh for ellipse Maximum bending moment V’s height of fill (including self weight) Maximum strain V’s height of fill (including self weight) M* = 33,000kN/m2 Ring Compression for M’ = 67,000kN/m2 arch Ring Compression for M’ = 67,000kN/m2 ellipse Maximum compressive thrust above and below thrust beam vs height of cover Maximum compressive thrust above and below thrust beam, up to 5.5m Maximum Strain V’s height of fill (including self weight) M’ = 67,000kN/m2 Maximum strain V’s height of fill (including self weight) M’ = 200,00kN/m2 Ellipse - Bending Moments Including self weight for M’ = 33,000kN/m2, 67,000kN/m2 and 200,000kN/m2 at a height of cover of 5.48m. Ellipse - Inner and Outer Fibre Strain including self weight for M’ = 33,000kN/m2, at 5.48m height of cover Arch - Bending Moments Including self weight for M’ = 33,000kN/m2, 67,000kN/m2 and 200,000kN/m2 at a height of cover of 5.48m. Arch - Inner and Outer Fibre Strain including self weight for M’ = 33,000kN/m2, at 5.48m height of cover

List of Tables in Appendix C

Table C-1 Table C-2 Horizontal Springline Deflections Table C-3 Table C-4 Table Showing Critical Ring Compressions and Normal

Table C-5(i),(ii) & (iii)

Comparison of Design Methods

Comparison of Vertical Crown Deflections

Pressures Corresponding to Predictions of Buckling Failure Table Showing Principal Structure Types Reviewed

GLOSSARY

Largekong Span Structure Buried corrugated metal structures of span greater than 7 metres.

Top Radius

Rise

Radius of curvature of plates forming the crown of the structure.

Vertical height from the lowest part of the corrugated plates, to the crown.

Top Rise Vertical height from the spring line to the top of the crown.

Ring Compression Axial load in pipe wall.

Side Radius Radius of curvature of plates forming the side of the structure.

Thrust Beam Reinforced concrete beam cast against corrugated plates either side of the crown.

Low Profile Arch Arch which has the side plates supported on footings.

High Profile Arch Arch which has the side plates supported on a further section of corrugated plating which has a radius of curvature equal to that of the crown plates.

Spring Line Horizontal line through the points of maximum span.

Free Field Pressure Vertical soil pressure equal to bulk density of soil multiplied by depth of soil to the point in question.

NOTATION

Total area of overburden material above the spring line, over the span of the structure, where W = yA.

Soil bending stiffness where C= 0.5M.

Structure span. RT

Twice top rise.

Young's Modulus of steel.

Compressive stress causing elastic buckling.

Height of cover above the top of the crown.

Second Moment of Area.

Number of wavelengths in buckle.

Constrained soil modulus.

Ring compression below thrust beams.

Ring compression corresponding with buckling failure.

Ring compression above thrust beams.

Soil pressure corresponding with buckling failure.

Radius of the corrugated plates immediately below thrust beam level.

Radius of the corrugated plates forming the crown of the structure.

Structure span.

Total overburden load, or total weight soil above the spring line, over the span of the structure .

Bulk density of the fill material.

Milli-strain, strain x 10".

Shape factor.

. ..

A P P E N D I X B

a40 Large spa1 Structured

of Design Approaches Comparisol

n I I I I a\ \ I I I I -

I and Theories

LL

U 0

2 160

Is n

z

Q, >

Q)

0

- 5 120 -

80

51.6 40

0

-40

400

360

320

280 - N

E \ z

16

Cornparisod Between S.M.P./GLOC and A.A.SH.T.0. Structure Tofile - Elll,,se Type A r Bolted Con ection - 4 Bolts per oorrugation Soil Modulus - As Shonn

\ 152mm x51nm Corruga'ions, 7mrn Seam Streigth to Ar&o Design 45 Units of HB Load give a Crown Live Load Pressure of Sl.SkN/rr?

- A.A.S.P.T.O. Seam Strength Criterion

\

Span of Structure (ml

FIGURE B-1

440

HT. COVqR 1.5m

360

320

280

240

200

160

120

80

51.6

40

0

-40

I I I I I I - I

152mmx51r~m Corruga' ions, 7mm Seam Strength t o Arrico Design 45 Units of HB Load give a Cro Live L o a d Pressure oy 5 1 . 6 k N / d

\

A.A.S H.T.O. S e a m Strength Criterion

M*=IOO.OOOkF. / f~?

-. -

4

10 12 14 16 4 6 8 2

!

Comparis 'n Between

E-I! k A , A , . z - A e Bolted CO ec t ion - 400

Structureai)rofile -

U

24

22

2c

18

16

14

12

10

E

E

L

2

C 8 10 12 14 16 2 4 6

Span of Structure (m)

FIGURE B-3

24 Large Spln Structures Comparison of Destga Approaches

22 ve is Determiled y D f Flil 20kN/m3

\ Comparis 3n Between S.hl.P./GLOCK Structure Profile - Ellpse B Bolted Ccmnectlon - 4 Bolts per So11 Modiius - As Sbown

152mmx5 mm Corrugc tions, 7mm Seam Strength to Arnco Design

20

18

16 A A.S.H.T.O. Sea n - Stre igth Criterion

E

LL 14

I - - - .c 0 \

I I 12 14 16 4 6 0 10 2

Span of Structure (m)

FIGURE 6-4

and The0 ies i i

I and A.A.S.H.T.O.

corrugation

Gauge Data

I

f n W 0

2 12 - n 0

- z - a

5.L8m COVER A L L M* VALUES

-

0 N

-

0 m

c

W z c ;t

N Ln

cz. N c-

cz. c c

E c

c- r n c

. _.

cz. N

0 4

0. c

Q) F

c

r

4 e

m c

N c

c c

-a m c

- N c

9 N c

00 N

0. m

0 Ln -

c c

E/

In c c

- . . i t . . , .. C . . . ..-.., . .p . . . . .-... - . . . . . . . .. . .$?:I: . . C . . . - c c c

CI N

- 9 N

a3 m

L n

E

r- m

4 rn c

rr\ N

rn N c

Ln N a

m I- 3

\3 4 . L n

m '2

N m c

N N c

~

0 c c

e 0 c

G c

0 N c

0 E

D1 0

FIGURE 8-5

!nt/Scheme 7.R.L. - DESIGN OF LARGE RRUGATED BURIED STEEL STRUCTURES.

SPAN

wing Ti t le FINITE ELEMENT MESH FOR ELLIPSE 5 L 8 m COVER A L L M’VALUES

Stirling Maynard & Par tner ; Consulting Engineers Bretton, Peterborough

Drawn C.D.J Scale N.1.S Date 17.4.90 Page Drawing No. 103 a

1 7 a3 -0 c

m l-

N rc

-0 a c

c rc

4 9 c

rn 9 c - N z

m c

“/F/“ M t- F

N t- c

c

c P

c 9 F

L n 9

a

i I 0 FIGURE 6-6

1' \ I I I I I I I \

// I I

I .c 0

N I P

D

4-

Max. Bending Moment v's Height of Fill (Inc. S.Wl For Arch/Elllpse For All Data Up To 17.6m For M*33,000kN/$ Backflll Run R e f . IUOR, 22(2)R.

Q) c 01 n c 0 .I

0) Q) > > + I

FIGURE B-7

Max. Strain V‘s Height of Fill (Inc. S.WJ For All Data Up To 17.6m For M+33,000kN/d Backflll For Arch and Ellipse Run Ref. 16(0, 22t2)R.

(D r I I I I 1

0

a2 > I

FIGURE 8-8

c

,3

Ring Compression (inc. S.WJ For M * 6 7 , 0 0 0 k N / d Backflll For Normal. No., and Large Thrust B e a m Run Ref . 2(D, 3KDRR. 321DR (Lad Load Step) Arch.

Nodes

Position of- Normal Thrust Bern

FIGURE B-9

-100

-200

0 I d

t I

Large TI E-300 \ z x ,+ Normal

-600

-700

Nodes

Ring Compression (inc. S.WJ For M + 6 7 , 0 0 0 k N / d Backfill For Normal, No, and Large Thrust Beam Run Ref. H2)R 332). 3 4 2 ) R R (Last Load Step1 Ellipse.

FIGURE B-10

0 0 OD N

0 0 d (U

0 0 0 (U

m I 4 4

Helght of Cover

'4 i

I 0

\

\ \

\ \ \ 5\

\ \ \

0

U) 8

\

E O(

I

v) 7

U 5 a ta 0 +

I ( Obl I

FIGURE B-12

Y

4

I I I I I

I

/ /

/ /

Max. Strain V's Height of Fill (Inc. S.WJ For All Data Up To 17.6m For M*67,00C kN/& Backfill F o r Arch and Ellipse Run Ref. 1710, 2 3 2 ) R .

0 - 9 I

I

cr! - I

FIGURE B-13

Max. Strain V's Helght of Fill (Inc. S.WJ For All Data Up To 17.6m For Mw200,OC k N / d Backflll For Arch and Ellipse Run Ref. IW, 24I2)R.

FIGURE 6-14

n 5 C

m I

N.B. Dlagrams Not To Scale. Run Ref. 7(2)R, 812)R, 9 (2 )R . Last Load Step 5.48m.

i 01

FIGURE 6-16

0 I- c 0 z

FIGURE B-17

+

I

c 2 U

0 i-

0 z L

FIGURE 8-18

A P P E N D I X C

TAOLE C . 1 COtlPARISON OF OESICN HETHODS

OESICN ? O N OURE

SPEC I A1 REOUIREHENIS SPEC1 11 RLOUlREHENlS OF OfS'CN FOR LONG SPAN FOR OEAO A N 0 LIVE I SIRUCIURES LOAOING

INIENOEO SCOPf nflltoo

, 1 4 4 OR WML PAN

3.140 8ASfO OH I I I f S P A N Of Ilf SlRUClURE ' 4 f w

.7S*l.El I 1 . L . I

I .B1 11.1. I BASfO OM P I IIF . No1 IV PAOlLIS con.

I f .0.S. HIHIHUM tmci OF

COVER 'REOUIREHCIIIS BlKKLlYG

- 1

U01 A f f l I C . 10 LWC SPAN SIRUCIMf

EXlENl OF OACKF ILL DbCKf 111 SPECIF ICAllON

IN114)r( COVLR 01 SIRUCIuRf L C R f l L l IS P A W I C W 300. . IllCH fVER IS P E A I C R .

ACKf ILL S O I L O f N S l l I M I N I M B S I ff SIAWARO [HSIIY EASfO M AASHIO 199. I O R LONG SPAN IRUClLIRfS. CRA01K 10 CWLI U I I H A A I H I O 14s QWS 1-1.1-3.1-7-4 kW A-7-S CWAC1f0 0 301 I!BO

I ... . .

No1 I N C L ~ t O I LWt P A N SlMlUIfS AS A I S I 1964 I MII IMLKlfO I A.I.S.I. L C K f l L L SOIL O f N S l l I M l N l M c OS1 Of IAWARO O f N S l l I BASfO M A.A.S.H.1.0. 119

mus ff PASsIvf SOIL 'L' wS1 Ef 613 BACKFILL n l N I M I I I O f N S l l l 901

HI nlYlMJI COVfR fOR OfSlU OAOS SHALL Bf SPAN16 BU1 WI I f S S IHAW 305.a tat

A W L I C . 10 LONG SPAN SIPUCILN Wl1H P f C l A L ILAlUIfS

IAWARO L.A.S.H.1.O. 199. 1HlS IS fOR BOlH lmR1 AW LOMC SPAN SlRUCIURfs

SFf C I A1

I W1 LPFLIC. 10 LMC SPAY SIRKIUR U l l H SPfCIAL ffAlLl7fS

-

1.144 IOR WRML P A N SlRUClUR

M MlMlM OCPllt Q C O W EASUREO fRDn t l f W M ;URfACf 10 IHf CROWN of 1IE ilRUClURf IS MII LfSS IHAN

XfAIfR. SlOf flll S I u L l :XlfMI 10 1 H(ICH1 ff SPAWI R I, MtCMVfR IllE CREAIfR R 10 1M FWItAllON LfVfL ff IIIE RDAO I f IHIS IS 1OMR.

PANIS OR &so.., witwin

-i--l-- I

.I I SPAN a( 111141 Slot ff 1M IWlUIf. IHlS IS 116 SAJlf IOR )HC SPAN SIRKIURfS I IM M l N l l U l DEPIH ff COVCR

WLL BE IHE LARCIR ff I

l l1H A M I N I M ff 600..

1I * SPAN I C I 1.56-1.6 1o.c. I

I1 SPfClf IEO

I W IOlAL LOAO Y M N SIMlUIf IS mxclfo 11 LOW f ILL

c

Table C-2 Horizontal Spring Line Deflections

o w - 5 h

9 N

I-

m -d

d

m m

w i l

H Z R H C i U w a avl

o x

2 "

- 5 Z H w m

H m a 3 i l a w x U H

d .-I

r(

N

Ln

m 4

Ln

m 4

N

4 N

N m

Q)

m N P

a I- m

tn c 0

* m rl w a, n

n x W U H O z s n l w a a x avl

4

4 m m

-

m N m

rl m u .-I U o w

- E ic a, > 0 w

m P

m 4 4

m P 4

I-

m N

m m (U

l-l

l-l m m

m I U a, 4 P m H

* m Ln m m

- 4

N 4

- 0 0 0

0 0 N

.

N a)

N

- a)

Ln

Ln

m 4

a)

m N P

m UY hl

m 4 m

m m

m N m

f

In c') 4

m

Q)

m

P (v

tD

4

N l-l

0 0 0 m m

. 0 0 0

P a

4 z 1 I c I /z

U 4 3 CI c r

- a > >

U 0 E - In h 0.

U b l In

2 - h

E

[I c

c c

t al L 3

Q

d .- .c

I I C

I I! c U \ z? m c .-

I - h M M In

-

9 3. 9

U 0 Q c

m h 9

c

d - 1

L 0

rn C 0

U

.- Y .- -E

c 0. (0

L

0 U

n

m C L l c

I N. U

3 3 n r

- D N m

U 0 2

-4 U m r-

.- P B al

9 M N 9

L L 0 U

In h 0.

c U N U d In al

L

rn In a

vt In c - / e c

U L n d

t 0 C

= I - U 0

2 -

0. Pl N

m A 1q; In c P

m v) '

0 .- a o u N rn a U L n 5 U

W " R U

n F

'74 M U \ ;L

0 9 vt

N - m c .- L

m M

z In c - 9 0. "

U 0 2 - In h 0

d

Q U .L

U .- L U

C

I 0 r In

0

m .-

d

% c

I U \ z - 0 M 2

I c I -

U 0

2 - 0. m N

- o h U2:

- 0 N C N a 0

u a w a l a L m u m v ,

.L

vt rc Q N

In

2

rn In 2. m c U.c U W L n U

.- d

o r 8

2. *- U Q W E m

Shape

E l l i p s e

Arch

Arch

Arch

0 imens i ons

8.2m span 4.9m r i s e

5.5m t op rad ius

15.5m span 7.9m r i s e

9 . lm top rad ius

7.9m span 4.6m r i s e

5.03m t op rad ius

As above

Special Features

Re l i ev ing Slab

Extent o f F i l l Height Cover

4 metres 0.9 metres

E l l i p s e

C i r c l e

E l l i p s e

i r c h Dipe

9rch

7.62111 span 7.62m r i s e 3.81111 top rad ius

7.77111 span 7.77171 r i s e 3.89111 top rad ius

7.24m span 4.06m r i s e 4.87m top rad ius

8.687m span 5.436m r i s e 4.44811 top

rad ius

11.532m span 4.775~1 r i s e Not Known

None

Rib S t i f f e n e r s

Not Ctear 1 . 5 m ht cover

4.879 metres 0.60 metres 0.73 metres

Compaction Wings 6.096 metres 3.353 metres

l h r u s t Beam St ruc ture on ?e ta in ing Wal ls

8 metres 2.1 metres

b c h 11.8m span 4.7171 r i s e 27.4111 top rad ius

- Date

- 1973

- 1974

- 1974

- 1974

- 1975

t 73.8kN/m 122kN/m

~~~

I tem Reference No.(R-)

Review L i t e r a t u r e No.(RL-)

F i e l d Test Laborator Model Computer Model

yHRT

1. Performance o f a l a rge corrugated s t e e l c u l v e r t RL1

146 tonne and 7 3 . 5

(22% d i f f ) tonne l o r r i e s F i e l d Test 99kN/m

2445 kN/m

670kN/m

Thrust beams S t i f f n e r r i b s Squeeze b locks

2. Measurement o f s o i l a rch ing above a l a rge diameter f l e x i b l e c u l v e r t RL2

3. Measured performance o f new town creek c u l v e r t

R1

15.24 metres 13.4 metres

1.830 metres 7.010 metres

F i e l d Test 338kN/m

237kN/m 366kN/m

860kN/m (61% d i f f )

522kN/m (55% d i f f ) 732kN/m 4 months (50% d i f f )

22OOkN/m None

None Thrust beams F i e l d Test

As above As above ---I--- ~~

4 .Computer Ana lys is o f Newtown Creek Cu lve r t R2

522kN/m 573.4kN/m - 1 670kN/m Computer Model

(41% d i f f )

Sa. S o i l Steel S t ruc tures Response t o l i v e loads . RL3

None White Ash Creek F i e l d Test

L i v e Load Tests Revealed l i v e load t h r u s t Measured around the Conduits a re almost neg l i g i b l e below the sp r ing l i n e l eve l .

Considers var i ous d i s t r i b u t i o n o f l i v e load

Not Clear 1.5m h t cover

5b. S o i l S tee l S t ruc tures Response t o l i ve l oads . RL3

Deux Riveres F i e l d Test

1975

- 1975

- 1980

- 1979

None The bending s t resses computed from the observed s t r a i n i n g were found t o be n e g l i g i b l e . Allowance should be made f o r dynamic load ing t o take i n t o account i r r e g u l a r i t i e s i n the r i d i n g surface.

Considers var ious d i s t r i b u t i o n o f l i v e load

Not Clear 1.25m ht cover

5c. S o i l Steel S t ruc tures Response t o l i v e l oads . RL3

Adelaide Creek F i e l d Test

Considers var ious d i s t r i b u t i o n o f l i v e load

49.52kN/m 138kN/m 50.71kN/m 45.0kN/m 162kN/m 90 Tonne 149kN/m (72% d i f f ) Ax le Loading

367kN/m 450kN/m 480kN/m 308kN/m 473kN/m None (34% d i f f )

The shor t term s t a t i c load t e s t s revealed o n l y 70 Tonne l o r r y small de f l ec t i on . The tes ts a l s o i nd i ca ted t h a t o n l y 29OTonne lorry a smal l p o r t i o n o f the l i v e loading reaches the sp r ing l i n e . -~

_ _ _ ~

6. F i e l d Tests of Long-Span tluminium Cu lve r t

RL4

F i e l d Test

7. Performance and 4na lys is o f a .ong-Span Cu lve r t RL5

F i e l d l e s t

3. Heavy Veh ic le .oading o f Arch St ruc tures o f Corrugated Metal RL6

F i e l d Test 1982

- I

Table C-5 ( i) D e t a i l of the p r o f i l e geometry o f f l e x i b l e c u l v e r t s and the tabu la ted f i nd ings from techn ica l papers, f i e l d t e s t s and computer models 1 c. P

y W 2 yA/2 y H R T Top Crown Thrust

Spring L ine I n v e r t Thrust

Shape

E l l i p s e

Dimensions Special Features

8.76111 span Re l i ev ing Slab 4.9501 r i s e 5.7m t o p rad ius

F i e l d Test

F i e l d Test Quy Water

F i e l d Test Stone H i l l

l abo ra to ry Mode l

1983

1988

1988

1970

E l l i p s e

E l l i p s e

7m span Stee l Angle 4.3m r i s e Ribs 4.4m t o p rad ius

9.83111 span Thrust Beams 6.76m r i s e F l e x i b l e and 6.227mto~ rad ius Concrete Road

7.47m span 4.19111 r i s e 5.03111 t o p rad ius

Var ious smal l model arches.

Thrust Beams F l e x i b l e Road Surface

~~ ~

F i e l d Test Computer Model

Not Known

Arch 11.710111 span S t i f f e n e r r i b s 4.801111 r i s e St ruc tures on

top o f r .c. stem wal ls.

89.23kN/m

NE FE VALUES ONLY

233kN/m l l3kN/m 189.67kN/m 292kN/m (35% d i f f )

A l l Shapes

De f lec t i ons a re no t r e l i a b l y est imated by ca l cu la t i on , must adopt F.E. approach. Placement and compaction o f b a c k f i l l i s o f major i n f l uence on c u l v e r t behaviour. p roper t i es , t he re fo re f i e l d t e s t s and labo ra to ry s o i l t e s t a re very important. independent o f the s o i l model adopted.

Re l i ab le p r e d i c t i o n o f c u l v e r t performance requ i res proper mode l l ing o f the s o i l P red ic ted t h r u s t s t resses are r e l a t i v e l y

E l l i p s e General I n f o .

A comparison o f compaction induced stresses in the s o i l and a s imple s o i l model demonstrated the major d i f f e rences in bending s t resses and d e f l e c t i o n . Model w i t h compaction induced s t resses c o r r e l a t e d reasonably we l l w i t h s i t e measurements o f e l l i p s e .

L i v e Load Tests

Extent o f F i l l Height Cover

F i e l d Test Laborator Model Computer Model

F i e l d Test

I tem Reference No.(R-)

Review L i t e r a t u r e No.(RL-)

202kN Ax le loading

6.05 metres 1.49111 - 1.69111

9.1ive l o a d Response o f a S o i l S tee l S t ruc tu re with a Re l i ev ing Slab RL7

107kN Ax le loading

3.5 metres 0.91 metres

10. Performance Eva lua t i on o f a Rib Reinforced Cu lver t RL8

1la.Load Tests on Two Long Span Corrugated Stee l Cu lver ts

R24

The r e s u l t s show t h a t t he road cons t ruc t i on has a major e f f e c t on the s t r u c t u r a l response o f t he c u l v e r t . V e r t i c a l d e f l e c t i o n and bending s t r a i n s f rom the l i v e loadings are ve ry small. The l i v e l oad t h r u s t s t resses almost i n s i g n i f i c a n t a t t he base/lower sec t i ons o f the cu l ve r t s .

455kN Ax le loading

9.8 metres 1.9 metres

Surf ace

I 7.47 metres 0.95 metres

455kN A x l e loading

1lb.Load Tests on Two Long Span Corrugated Stee l Cu lver ts R24

Arch

Arches

As Above

Back ana lys i s o f l abo ra to ry t e s t f i n d i n g s revea led t h a t the p r e d i c t e d values from B012/82 were conservat ive f o r s t r u c t u r e s with he igh ts o f f i l l g rea ter span /7.

12. Some Research on Underground F l e x i b l e Arches

R3

13. Measurements and Ana lys is o f Compaction e f f e c t s on a long span Aluminium c u l v e r t R5

I

1.219 metres 0.762 metres

1/15

General Comnents

1980 14.Large Bur ied Metal Culvert Design and Construct i o n

R22

General 9 15. F.E. Ana lys is Compaction Induced Stresses and Deformations

Table C - 5 (ii) D e t a i l o f the p r o f i l e geometry o f f l e x i b l e c u l v e r t s and the tabu la ted f i n d i n g s from techn ica l papers, f i e l d t e s t s and computer models

Special Features Extent o f F i l l Height Cover

yHS/2 yHRT Top Crown Spr ing L ine yA/2 Thrust I n v e r t Thrust

F l e x i b l e road surface

5.95 metres 0.7m - 1.2m

Lean concrete and f l e x i b l e road surface

3.7 metres 0.86 metres

~~

A l l Shapes

~~~~

Reported Fai lures:- A l l f a i l u r e s repor ted on cu l ve r t s with th rus t beams have been a t t r i b u t a b l e t o poor b a c k f i l l , which subsequently was shown not t o be in accordance with Armcols Speci f icat ion. su f fe red from f rozen s o i l and snow and i ce inc lus ions in the b a c k f i l l . A l l cases o f f a i t u r e were repor ted dur ing the cons t ruc t i on stages and no repor ted cases o f f a i l u r e in serv ice condi t ions were reported.

Many o f the condui ts constructed in Canada have

Pipe Arch

Arch

3.805111 span Thrust Beam 2.640111 r i s e 2.030mtop rad ius

l l m span None 6.5m r i s e 36.53 metres 920kN/m 993kN/m

836kN/m NE FE Values Only 15 tonne

548kN/m I 959kNIm l o r r y load.

7.80111 span 6.92111 r i s e 3.75111 top rad ius

10.78m span 7.13m r i s e 7.5171 top rad ius

Thrust Beams

Thrust Beams

PO.lkN/m 13lkN/m

475kN/m

174kN/m 86.6kNim 215kNIm 126kN/m

564kN/m 629kN/m 500kN/m 250kNIm 900kN/m (-100% d i f f ) long term 900kN/m

(ong term (0% d i f f )

- Date

- 1989

L i v e Load Tests

I tern Reference No.(R-)

Review L i t e r a t u r e No.(RL-)

F i e l d Test Laborator Model Computer Model

Shape D i mens i ons

16a. The e f f e c t o f pavement layers on the behaviour of corrugated s t e e l c u l v e r t s RL24

f i e l d Test My t ho l mr oyd

Arch 5.95m span 4.63111 r i s e . 3.01m top rad ius I t was concluded that the Glock ana lys i s method gave a

more r e a l i s t i c f ac to r of sa fe ty against the buck l i ng than B012/82. The pavement reduces l i v e load d e f l e c t i o n and bending moments recorded. The l i v e load f l e x u r a l s t r a i n s and l i v e load crown de f lec t i ons made very l i t t l e d i f ferences t o the r i n g compression s t r a i n s .

120kN - 455kN on a s i n g l e ax le F i e l d Test

Puy Footpath 1989 Arch 3.7m span

3.36111 r i s e 1.53111 top rad ius

16b. The e f f e c t o f pavement layers on the behaviour o f corrugated s t e e l c u l v e r t s RL24

17. Review of the Design and Construct ion o f Long Span Corrugated Metal Bur ied Culver ts R22

1977 Review

1981 >3.805m 1.5m

1 /3 18. Loading Tests on an Armco Pipe Arch Cul v e r t

F i e l d Tests

Large bending s t r a i n s were recorded i n the c u l v e r t before l i v e loading as a consequence o f the conlpactive e f f o r t . L i ve load v e r t i c a l crown de f lec t i ons were very smal l f o r he igh ts of f i l l between 1 .5m and 0 . h L i ve load bending s t r a i n s were a l s o very small as compared t o dead load e f fec ts . There appears t o be a l i n e a r Iogor i thmic l i v e load bending s t r a i n and d e f l e c t i o n r e l a t i o n s h i p w i t h he ight o f f i l l . R29

15.2 metres 7.6 metres

19. S t ruc tu ra l Evaluat ion of New Concepts f o r Long Span Culver ts and Culver t l n s t a l l a t i o n R30

Review and Computer Analys is

1979

I I 2Oa. Long Term Behaviour of F l e x i b l e Large Span Culver ts Norway RL32

F i e l d Tests

k metres 1 . l m - 1.6m

5 metres C.2 metres

tob. l ong Term 3ehaviour o f F l e x i b l e Large Span Cu lve r t s Norway RL32

' i e l d 'ests

Table C - 5 (iii) D e t a i l of the p r o f i l e geometry o f f l e x i b l e c u l v e r t s and the tabulated f ind ings from technica l papers, f i e l d t e s t s and computer models

.. c z