precast lining design - swsglobal.com
TRANSCRIPT
PRECAST LINING DESIGNTechnical Booklet 01
“Our strategy is to escort and ensure our clients with a valuable design which allows to save money and time following the rules of art. We believe that it is necessary to balance a considered mix of good engineering design with exploration and innovation”
Nima NoroozipourSWS France Director
5 ∙ PRECAST LINING DESIGN
A CHALLENGINGDESIGN TASK
Shield tunnel is only apparently a simple construction with solid cylindrical shape; it is in fact an articulated structure made of segments arranged to form consecutive rings in staggered layout. Segments are usually bolted together at longitudinal joints to make up rings, which in turn are connected via dowels at circumferential joints.
Several modelling techniques exist to account for the presence of joints, each with diverse degree of accuracy: given the repetitiveness of tunnel construction, built as a sequence of multiple rings, even little optimization in the analysis of the single component may lead to significant overall cost reduction.
Mastering the available approaches thus allows tuning the analysis effort to the required design level, in order to satisfy Client’s requirements as appropriate.
LÄNGSFUGE VERSCHRAUBT M 1:2
BOLTED LONGITUDINAL JOINT scale 1:2
LÄNGSFUGE VERSCHRAUBT M 1:2
BOLTED LONGITUDINAL JOINT scale 1:2
BASISLÖSUNGBASE SOLUTION
RINGFUGE MIT STECKDÜBEL M 1:2
CIRCUMFERENTIAL JOINT WITH DOWEL scale 1:2
LÄNGSFUGE MIT FÜHRUNGSSTAB M 1:2
LONGITUDINAL JOINT WITH GUIDING BAR scale 1:2
RINGFUGE MIT STECKDÜBEL M 1:2
CIRCUMFERENTIAL JOINT WITH DOWEL scale 1:2
LÄNGSFUGE OHNE FÜHRUNGSSTAB M 1:2
LONGITUDINAL JOINT WITHOUT GUIDING BAR scale 1:2
VERBESSERTE TYP BIMPROVED LAYOUT TYPE B A7RM6-A RM6-A
30
3
10
7.5
3721
9910
22
33
10
99
198
400
200200
59.8
3.952
3.9
1.1
1.1 Ø50 8311
5
30
7.5
3724
22
33
3
R26
Kantenschutz aus GFKVTR Corner Support
FührungsstabGuiding BarL=400mmØ50mm
4040
3
37
200
200
30
3
10
10
7.5
3721
99
22
33
10
9930
10
7.5
21
22
33
Einsatz für SteckdübelDowel Sleeve
SteckdübelDowel
Achse StreckdübelAchse Tübbing
Kantenschutz aus GFKVTR Corner Support
33
198
400
106.2
8VAR.
60
124
449.7
74.1
175
25°
311.7
34.7
45
139.9
21
Ø34.9
20.6°
30
41.7°
40
50.1
198.1
225
98100.9
2.9
Nut für Dichtprofil aussenExternal Gasket Groove
SchraubentascheBolt PocketSchraubentasche
Bolt Pocket
SchraubendübelBolt Sleeve
Kantenschutz aus GFKVTR Corner Support
Nut für Dichtprofil inneninternal Gasket Groove
SchraubenSteel Bolt
200
200
5.2
2.1
Achse StreckdübelAchse Tübbing
26
10 3
129.2
129.2
29.8
30.8
310
10
258
26
10 3
330
.8
5.2Kantenschutz aus GFKVTR Corner Support
22
8
2.72.7
2.1
Einsatz für SteckdübelDowel Sleeve
SteckdübelDowel
258.4 400
29.8
5.2
8
129.2
10.3
2.126
10.3
129.2
258.4
200200
24.882.1
26
10
330
.8
10 3
30.8
5.2
3
InjektiionsschlauchInjection Pipe
Kantenschutz aus GFKVTR Corner Support
2
3
2
3535
2.72.7
VTR Corner
Bolt PocketSteelBolt Bolt Sleeve
InternalGasket
External Gasket
> ABOVE: TYPICAL DETAIL OF A BOLTED LONGITUDINAL JOINT (BBT project)
> LEFT PAGE: DETAILED REPRESENTATION OF A UNIVERSAL RING (6+1 layout)
7 ∙ PRECAST LINING DESIGN
Although precast tunnel lining is a modern construction technique, the underlying structural concept is much less recent.
In fact, tunnel rings are arranged in a staggered layout to prevent longitudinal joints being in the same position, and this configuration allows mutual force transfer between rings, typical of 3D reciprocal frame. These structures date back to Mesopotamian Era and have been further studied by Leonardo da Vinci.
Rationale of tunnel lining reciprocity is that single rings with internal hinges (i.e., longitudinal joints between segments) are inherently unstable. Only the connection of multiple rings makes the tunnel statically determinate, provided the joints are staggered, otherwise the entire tunnel becomes unstable.
AN ANCIENTSTRUCTURAL CONCEPT
Key Segment
GuidingBar Groove
Circumferential Joint
Longitudinal Joint
Base Segment
Standard Segment
> ABOVE: CONCRETE LINING INVENTOR MODEL (KOVALINCH project)
> LEFT PAGE: TRI RF-UNITS RECIPROCAL STRUCTURE CONCEIVED BY LEONARDO DA VINCI
9 ∙ PRECAST LINING DESIGN
TRADITIONALDESIGN APPROACH
For years, tunnel linings have been studied as solid rings with uniform flexural rigidity, thus ignoring the localized stiffness decrease at longitudinal joints.
This simplification allowed the development of analytical solutions, under specific loading conditions, and is generally able to provide safe design for tunnel segments.
The “solid ring” approach is in fact widely present in technical Standards and Guidelines, and refined by Muir Wood [1] via the introduction of a reduction coefficient for bending stiffness (an equivalent rigidity of the entire lining can reflect the reduction of rigidity at segment joints).
This traditional approach is still valid for many applications, but does not allow a precise definition of section force distribution between segments and joints, which may be required for specific needs and, in general, for design optimization.
[1] Muir Wood - The circular tunnel in elastic ground (1975)
> ABOVE: RS2 MODEL DEVELOPED FOR A MECHANISED TUNNEL (BBT project)
> LEFT PAGE: ALLOWABLE TUNNEL JOINT LAYOUT AND MOMENT TRANSFER MECHANISM
TOTAL DISPLACEMENT m
0.00e+0002.50e-0035.00e-0037.50e-0031.00e-0021.25e-0021.50e-0021.75e-0022.00e-0022.25e-0022.50e-0023.00e-0023.25e-0023.50e-0023.75e-0024.00e-0024.25e-0024.50e-0024.75e-0025.00e-002
-55 -52.5 -50 -47.5 -45 -42.5 -40 -37.5 -35 -32.5 -30 -27.5 -22.5 -20 -17.5-25-57.5
11 ∙ PRECAST LINING DESIGN
ADVANCEDDESIGN APPROACH
As a logical evolution of the traditional approach, actual joints between segments and rings are included in the analysis.
For instance, Japanese Standards [1] describe “multi-hinged ring models” and “beam-spring models”: the former simulate longitudinal joints as perfect hinges; the latter include rotational springs for joints between segments and shear springs for joints between rings. Although yielding evident improvement, these advanced approaches are far from being exhaustive as neglect the presence of friction and mechanical fasteners or require at least correct tuning of spring stiffness.
A further, possibly ultimate, evolution in tunnel design approaches may be the actual modelling of contact surface and the presence of mechanical fasteners, thus avoiding undesired analysis simplifications and definition of complicated adjustment techniques for spring stiffness.
[1] Japan Society of Civil Engineers - Standard Specifications for Tunneling: Shield Tunnels
> ABOVE: TUNNEL 3D FE MODEL WITH STAGGERED RING LAYOUT (STRAND 7)
> LEFT PAGE: TYPICAL REINFORCEMENT LAYOUT OF A TUNNEL SEGMENT
1st Ring of the series
Last Ring of the series
Circumferential Joint
Longitudinal Joint
CIRCUMFERENTIAL JOINT WITH BICONE SHEAR DOWELCIRCUMFERENTIAL JOINT WITH SPECIAL DOWEL
13 ∙ PRECAST LINING DESIGN
NON-LINEARJOINT BEHAVIOR
SWS followed this design evolutionary path until developing a modelling approach that simulates the actual non-linear joint behaviour.
The reduced contact surface between segments, due to gasket grooves and stress relieves, is modelled via “fibre elements” characterised by concrete nonlinear stress-strain relationship: in case of large thrust eccentricity in the ring, the contact surface further decreases as fibres in tension are progressively excluded by the solver.
Shear force transfer is modelled by friction at contact elements and eventually by bolt and guiding rod elements, if present.Connection between consecutive rings is simulated via dowel elements.
Inclusion of these technological components, with their respective stress-strain relationships, allows non-linear models to provide correct section force and deflection distribution along the ring and gives insight into the local performance of tunnel devices.
> ABOVE: SCHEMATIC OF SWS MODELLING APPROACH FOR LONGITUDINAL JOINTS
> LEFT PAGE: TYPICAL DOWEL CONNECTORS IN CIRCUMFERENTIAL JOINTS
A8
Linear Lining Element
y
zxLining Axis
B segment
B joint
Non - Linear Fibres (σn)
Non - LinearConnection (τ)
SIMPLIFIED DESIGN APPROACH
APPROXIMATE EVALUATION OF JOINTS PERFORMANCE
CONSERVATIVE FORCE CALCULATION POTENTIALLY RESULTING IN
NON-REQUIRED BOLTS INSTALLATION
APPROXIMATE ESTIMATION OF CONCRETE LINING
WATER TIGHTNESS
> ABOVE: SCHEMATIC COMPARISON BETWEEN SIMPLIFIED AND SWS DESIGN APPROACHES
SWS DESIGN APPROACH
ACCURATE EVALUATION OF JOINTS PERFORMANCE
DESIGN OPTIMISATION POTENTIALLY LEADING TO NO BOLTS INSTALLATION
ACCURATE CALCULATION OF CONCRETE LINING
WATER TIGHTNESS
ACHIEVEDADVANTAGES
SWS design method allows optimization of precast segment design because, unlike simplified approaches, the actual distribution of forces between segments and joints is accounted for, without need for spring stiffness tuning required by codified advanced approaches.
Furthermore, forces in the mechanical fasteners and guiding rods between segments are directly determined by the solver, making their check straightforward.
Longitudinal joint check against compressive stress in the contact surface is automatically verified by convergence of non-linear analysis.
Finally, detailed modelling of contact surface provides strategic information on the pressure distribution within longitudinal joints, necessary to evaluate gasket water tightness and overall tunnel sealing performance.
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