第十五屆大地工程學術研究討論會論文集(Geotech2013)
Proceedings of the 15th Conference on Current Researches
in Geotechnical Engineering in Taiwan
中華民國 102 年 9 月 11-13 日, 雲林, 台灣
September 11-13, 2013
Yunlin, Taiwan
Geotechnical Analysis for Static Liner Design of the World’s Largest
Diameter Soft Ground Bored Tunnel in Downtown Seattle
Mike Swenson1 and Barry S. Chen2
1
Senior Geotechnical Engineer, Hart Crowser, Inc., USA
2
Senior Principal, Hart Crowser, Inc., USA
Abstract
The State Route (SR) 99 Tunnel in Seattle will be the world’s largest diameter bored tunnel. The 17.1-m-diameter
(56 ft), 2,835-m-long (9,300 ft), bored tunnel crosses under downtown Seattle, reaching depths of 66 m (215 ft). The
bored tunnel alignment traverses variable glacially overconsolidated soil deposits, and groundwater pressures at the
tunnel invert will be as high as 5.2 bars. The tunnel will replace the SR 99 Alaskan Way Viaduct, which was
constructed along Seattle’s waterfront in the 1950s. The double-deck viaduct structure had been deteriorating and was
further damaged in the 2001 Nisqually earthquake. This paper discusses the geostructural analytical approach to the
precast concrete segment liner design, focusing on the geotechnical analyses for static liner design. Geotechnical
evaluations included numerical modeling of ground relaxation, existing and potential future building loads, and
soil-structure interaction springs for varying geologic conditions.
Key Words: Bored Tunnel, Liner Design, Numerical Modeling
stadiums for Seattle Mariners and Seattle Seahawks. It
extends north along the Alaskan Way Viaduct, crosses
beneath the Viaduct, and passes under downtown Seattle.
The bored tunnel emerges north of downtown just east of
the Seattle Center and the Space Needle. Development
along the alignment consists of on-grade and elevated
roadways, buildings ranging from single-story to
high-rise developments, railroad and sewer tunnels, and
public and private utilities.
The bored tunnel will be approximately 2,835 m
(9,300 ft) long. The tunnel will be excavated by an Earth
Pressure Balance (EPB) Tunnel Boring Machine (TBM)
with a 17.5-m-diameter (57.5 ft) cutterhead. The tunnel
liner will have an outer diameter of 17.1 m (56 ft). At its
lowest point, the tunnel crown is at elevation –29 m
(–95 ft), and is 66 m (215 ft) deep at its greatest depth.
This paper discusses the geo-structural analytical
approach to the precast concrete segmental liner design,
focusing on the static geotechnical analyses.
Geotechnical evaluations included numerical modeling
of ground relaxation, existing and potential future
building loads, and soil-structure interaction springs for
varying geologic conditions.
1 SR 99 TUNNEL PROJECT
The State Route (SR) 99 Tunnel is being
constructed under a design-build contract as part of the
Washington State Department of Transportation’s
(WSDOT) Alaskan Way Viaduct Replacement Program.
The SR 99 Alaskan Way Viaduct is an aging
double-deck highway structure in Seattle, Washington
that was built in the 1950s. The Viaduct has been
deteriorating due to the age of the structure, as well as
damage resulting from the 2001 Nisqually earthquake.
The SR 99 Tunnel Project consists of three segments:
South Approach, Bored Tunnel, and North Approach.
The South and North Approaches consist of
cut-and-cover tunnels and U-sections. This paper focuses
on geotechnical analyses for static liner design of the
bored tunnel segment.
The new SR 99 Bored Tunnel alignment is shown
on Figure 1 in plan view and on Figure 2 in profile view
(tunnel stationing is in feet). The bored tunnel begins
south of downtown Seattle immediately west of the Port of
Seattle’s Terminal 46 on Elliot Bay, near Seattle’s Pioneer
Square Historic District, and northwest of the two sport
1
第十五屆大地工程學術研究討論會論文集(Geotech2013)
Proceedings of the 15th Conference on Current Researches
in Geotechnical Engineering in Taiwan
Scale in Feet
0
0
Scale in Meters
中華民國 102 年 9 月 11-13 日, 雲林, 台灣
September 11-13, 2013
Yunlin, Taiwan
2000
400
Puget Sound/
Elliott Bay
Space Needle
Pike Place Market
Terminal 46
SR99 Bored Tunnel
Lake
Union
Downtown
Seattle
Pioneer Square
Historic District
CenturyLink
Field
Interstate 5
Figure 1 Plan view of SR 99 Bored Tunnel alignment
colluvial processes, and several natural lakes developed as
the glacier retreated.
As part of the historical
development of Seattle, substantial regrading efforts were
undertaken in the late 19th and early 20th centuries, which
cut hills and filled valleys and tidelands, generally by
hydraulic placement.
While the excavations and structures for the
approaches at the north and south ends of the bored
tunnel must contend with significant depths of recent,
normally consolidated soils and fill, the bored tunnel
generally lies within glacially overridden soil deposits.
These deposits are often highly variable within relatively
short distances due to the variability in erosion and
deposition during the multiple glacial events and
interglacial periods.
The soil deposits were grouped into Engineering
Soil Units (ESUs) based on their geotechnical
characteristics. The ESUs along the SR 99 Bored Tunnel
alignment are briefly described in Table 1, and the
design geotechnical properties for the ESUs are
presented in Table 2. A subsurface profile showing the
distribution of ESUs along the bored tunnel alignment is
provided on Figure 2.
2 GEOLOGIC/SUBSURFACE
CONDITIONS
2.1 GEOLOGY
Seattle is located on Puget Sound in the Puget
Lowland between the Olympic Mountains to the west
and the Cascade Range to the east. The Puget Lowland
has been subject to several glacial advances during the
Pleistocene Age (2 Ma – 10 Ka) (Galster and Laprade
1991). The resulting geology is a complex of glacial and
non-glacial soils. All but the most recent recessional
glacial deposits and non-glacial deposits have been
overridden and overconsolidated by glacial ice. The most
recent glacial advance is estimated to have had an ice
sheet approximately 1,000 m (3,000 ft) thick, though only
a fraction of this thickness is estimated to have contributed
to the overconsolidation of overridden soils due to the
pressures in subglacial meltwater (Booth 1991).
The north-south trending, elongate hills and valleys
left behind by the last glacial advance and retreat were
partially eroded and filled naturally by alluvial and
2
中華民國 102 年 9 月 11-13 日, 雲林, 台灣
September 11-13, 2013
Yunlin, Taiwan
Vertical Exaggeration x 5
1 Engineering Soil Unit (ESU)
Top of Glacially Overridden Soils
3
1
7
6
4
5
8
2
第十五屆大地工程學術研究討論會論文集(Geotech2013)
Proceedings of the 15th Conference on Current Researches
in Geotechnical Engineering in Taiwan
Figure 2 Subsurface profile and design geologic sections along SR 99 Bored Tunnel alignment (adapted from
WSDOT 2010 and STP 2011)
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第十五屆大地工程學術研究討論會論文集(Geotech2013)
Proceedings of the 15th Conference on Current Researches
in Geotechnical Engineering in Taiwan
Table 1
Recent Deposits
Stress
history
Description
Engineering
Soil
Units
ESU
1
2
3
4
Glacially Overridden /
Overconsolidated
of
中華民國 102 年 9 月 11-13 日, 雲林, 台灣
September 11-13, 2013
Yunlin, Taiwan
5
6
7
8
Description
Highly heterogeneous mixture of sand, silt, and clay with peat and wood debris. Variable characteristics that can change
drastically within a short distance depending on specific content.
Loose to dense silt and sand with gravel. Includes normally consolidated alluvium, beach deposits, reworked glacial
deposits, and recessional ice-contact deposits.
Soft to very stiff low-plasticity clay and silt with fine sand interbeds. Includes normally consolidated estuarine deposits
and recessional lacustrine deposits.
Very dense or hard cohesive mixture of gravel, sand, silt, and clay. Includes glacially overridden till, glaciomarine, and
till-like diamict deposits.
Dense to very dense silty sand to sandy gravel. Includes glacially overridden glaciofluvial (outwash) deposits and
non-glacial fluvial deposits.
Very dense silt, silty fine sand, and fine sandy silt. Includes glacially overridden lacustrine deposits.
Hard, interbedded, low to high plasticity silt and clay. Includes glacially overridden glaciomarine, glaciolacustrine, and
non-glacial mud-flow deposits. Localized trace to abundant zones of sheared and fractured/jointed slickensided soil
attributed to glacial ice loading, stress relief upon unloading, and/or desiccation (Galster and Laprade 1991).
Dense to very dense, unsorted mixture of gravel, sand, and silt. Can have a similar appearance to ESU 4, but can vary over
short distances. Gradations include clean or relatively clean sand. Can be adjacent to and transition into ESU 4 and ESU 5.
(WSDOT 2010 and STP 2012)
2.2 HYDROGEOLOGY
3 DESIGN CRITERIA
There are two general aquifers along the bored
tunnel alignment. The upper aquifer is unconfined and
present in the recent, normally consolidated deposits and
often occurs as perched groundwater on underlying
glacially overridden soils. The lower aquifer is typically
confined at the elevation of the bored tunnel, regionally
recharged, and present in the glacially overridden
deposits. Groundwater flow is generally toward surface
water bodies that include Elliott Bay along most of the
alignment and Lake Union at the north end. The bored
tunnel alignment is almost entirely within the lower
aquifer. Based on seasonal variation of groundwater
levels measured near the bored tunnel elevation, an upper
bound groundwater elevation of 6 m (20 ft) was used for
liner design, resulting in groundwater pressures as high
as 5.2 bars at the lowest elevation of the tunnel invert.
The SR 99 Bored Tunnel Project contract identified
the minimum requirements for the tunnel geometry and
liner (WSDOT 2010). The required geometry of the SR
99 Bored Tunnel roadway is north- and south-bound
lanes in a stacked configuration with 9-m-wide (30 ft)
roadways, including two traffic lanes and shoulders, with
a minimum vertical clearance of 4.7 m (15.5 ft). The
required permanent tunnel liner consists of precast
segments with a minimum thickness of 0.6 m (2 ft), a
minimum of 1% steel reinforcement, and a 100-year
design life. The design liner geometry to meet the
roadway requirements is 15.8 m inner diameter (52 ft),
which requires a minimum 17.1 m diameter (56 ft) bored
tunnel.
The SR 99 Bored Tunnel Project contract identified
existing buildings and other structures that were required
to be analyzed in the liner design. For potential future
development, the contract also required evaluation of a
335 kPa (7,000 psf) building surcharge applied at the
height and width limits of WSDOT’s right of way above
the tunnel, which is to 16.5 m (54 ft) above the crown
and 25.6 m (84 ft) wide. Additionally, the contract
specified that the design analyses include evaluating the
zones of minimum depth and maximum overburden, and
analyses to account for the geologic and hydrogeologic
variability along the tunnel alignment.
For seismic design, two design earthquakes, the
Expected Earthquake and the Rare Earthquake, were
considered for the design of the tunnel liner. The
Expected Earthquake has a 108-year return period and is
associated with an Operational Performance Objective,
while the Rare Earthquake has a 2,500-year return period
and is associated with a Life Safety Performance
Objective. Under the Rare Earthquake, the objective is to
prevent collapse of the tunnel liner.
2.3 REGIONAL SEISMICITY
The seismicity of western Washington is dominated by
the Cascadia Subduction Zone in which the offshore Juan
de Fuca plate is subducting beneath the continental North
American plate. Three main types of earthquakes are
typically
associated
with
subduction
zone
environments—crustal,
intraplate,
and
interplate
earthquakes. Seismic records for the Puget Sound region
indicate a distinct shallow zone of crustal seismicity, the
Seattle Fault Zone, that may have surficial expressions and
can extend to depths of 25 to 30 km (16 to 19 mi). The
northernmost splay of the Seattle Fault Zone is
approximately 2.4 km (1.5 mi) south of the south end the
bored tunnel (U.S. Geological Survey 2006). A deeper zone
is associated with the subducting Juan de Fuca plate and
produces intraplate earthquakes at depths of 40 to 70 km (25
to 43 mi) beneath the Puget Sound region (the 1949,
Magnitude (M) = 7.1; 1965, M = 6.5; and 2001, M = 6.8
earthquakes) and interplate earthquakes at shallow depths
near the Washington coast (the 1700, M ~ 9.0 earthquake).
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第十五屆大地工程學術研究討論會論文集(Geotech2013)
Proceedings of the 15th Conference on Current Researches
in Geotechnical Engineering in Taiwan
Table 2
Recent Deposits
Stress
history
Design soil properties for the ESUs (WSDOT 2010 and STP 2012)
ESU
1
2
3
4
Glacially Overridden /
Overconsolidated
中華民國 102 年 9 月 11-13 日, 雲林, 台灣
September 11-13, 2013
Yunlin, Taiwan
5
6
7 - Intact
7 - Residual
8
Unit weight,
kN/m3 (pcf)
18.1
(115)
19.6
(125)
17.6 - 18.1
(112 – 115)
22.8
(145)
20.4
(130)
19.6
(125)
18.9
(120)
18.9
(120)
22.8
(145)
At-rest lateral
earth pressure
coefficient
Effective
friction angle,
degrees
Effective
cohesion,
kPa (psf)
0.45
34
0
0.40
36
0
0.5 - 0.6
25 - 32
0
0.6
40
240
(5,000)
0.8
39
0
0.8
39
0
1.4
25
57
(1,200)
1.4
15
0
1.0
40
0
Maximum shear modulus,
Pa (psf)
5.7 x 107
(1.2 x 106)
1.1 x 108
(2.3 x 106)
3.6 x 107 – 6.7 x 107
(7.5 x 105 – 1.4 x 106)
1.2 x 109
(2.5 x 107)
8.1 x 108
(1.7 x 107)
4.1 x 108
(8.6 x 106)
4.1 x 108
(8.6 x 106)
4.1 x 108
(8.6 x 106)
1.4 x 109
(2.9 x 107)
evaluating the minimum criteria using conservative,
simplifying assumptions; performing sensitivity analyses;
and concentrating geostructural analysis effort on critical
design sections to determine if a more robust liner was
necessary.
4 DESIGN METHODOLOGY
Because there were many structures and buildings
to evaluate, induced stresses in an elastic medium were
initially assessed as a screening analysis. This elastic
evaluation estimated the induced stresses at the tunnel
crown for groups of structures and buildings, due to both
structural loading and excavation unloading. Based on
these estimated induced stresses, upper- and lower-bound
influence cases were identified at the design geologic
sections. These upper- and lower-bound influence cases
were evaluated using static geotechnical numerical
models.
The general geostructural liner design methodology
used a two-step approach.
1.
Geotechnical numerical models were used to
determine static, unfactored soil and groundwater loads
and soil springs for soil-structure interaction used in the
structural design of the tunnel liner.
2.
Structural numerical models were used to
evaluate various limit states of the tunnel liner and
interior structure using the soil and groundwater loads,
and soil springs from the geotechnical modeling.
The purpose of the static geotechnical numerical
models was to assess the effects of geologic variability,
tunnel excavation and relaxation, and combinations of
structure, building, and future loads on the soil loads
transmitted to the liner. After reviewing these
evaluations, select sections were further analyzed to
evaluate seismic ground deformation using geotechnical
models and various limit states using structural models.
Because the contract provided the minimum liner
design criteria (i.e., 0.6 m (2 ft) thick, 1% steel
reinforcement), the liner design analysis focused on
5 STATIC ANALYSIS
Design geologic sections were selected to assess the
geologic variability along the tunnel alignment, as well
as topographic/geometric variability and building and
structure locations. Figures 2 and 3 show the 15 design
geologic sections.
Based on review of the tunnel alignment and
existing
structures
and
buildings,
including
considerations for significant basement excavations and
unbalanced loading/unloading conditions on the liner,
other buildings were identified for liner design
evaluations in addition to those required by the contract.
Also, tunnel deformation mitigation and buoyancy
resistance measures at the south end of the alignment
(South End Settlement Mitigation Plan, SESMP), which
include jet grouting, drilled shafts, and an uplift slab that
will influence loads on the liner, were evaluated. Figure
3 also shows all the existing buildings and structures
evaluated for the liner design (12 structures and 74
buildings).
Building and structure foundations vary from spread
footings and mat foundations to deep shafts and piles,
ranging from 2.4 to 19 m (8 to 63 ft) long and as close as
4.9 m (16 ft) above the tunnel crown. Buildings along the
tunnel alignment range from 4.0 to 166 m (13 to 546 ft)
tall with basement excavations ranging from
approximately 0 to 27 m (0 to 87 ft) deep.
5
第十五屆大地工程學術研究討論會論文集(Geotech2013)
Proceedings of the 15th Conference on Current Researches
in Geotechnical Engineering in Taiwan
中華民國 102 年 9 月 11-13 日, 雲林, 台灣
September 11-13, 2013
Yunlin, Taiwan
2 85+ 00
D es ig
n G eo
lo g ic
S ta ti o
S ec tio
n 28 6+9
n
3
270+00
e ct
g ic S
eolo
gn G
D e si
8+ 03
n 26
S t a tio
io n
260
+0 0
2 65 +00
ELLIOT BAY
INTERCEPTOR TUNN EL
SEATTLE MONORAIL
275 +00
e ctio n
e o lo g ic S
D e s ig n G
4 +4 8
S ta ti o n 27
s ig
e
n G
n
ct io
Se
g ic 2 59 + 68
o lo
n
ti o
S ta
25
5 +0
0
De
SR99 Bored Tunnel
BATTERY ST TUNNEL
280 +00
D es ig n G e o lo g ic S ec tion
S ta ti on 282+6 3
PIKE ST ADIT
0+
25
00
on
c ti
3
Se
+1
52
g ic
lo
n 2
eo
t io
n G Sta
s ig
n
on
c ti
3
S e 0+0
24
g ic
o lo t io n
Ge
S ta
ic
og
ol
3
G e 5+9
n
3
s ig n 2
D e t io
S ta
Se
ct
io
n
0+
23
Se
c ti
on
io n
2 20 +
215 +00
n
S e c tio
73
lo g ic
2 19 +
Geo
io n
S ta t
ic S ec tion
G eo l o g
2 11+ 5 3
S t at io n
SESMP
2 10+ 00
D e sig n
D es ig n G e o lo g ic S ec tion
D es ig n G e o lo g ic S ec tion
200 +00
S ta ti on 203+3 8
D es ig n G e o lo g ic S ec tion
S ta ti on 198+6 5
ALASKAN WAY VIADUCT
2 05+ 00
S ta tion 206+4 8
195+00
0
200
Scale in Meters
Scale in Feet
0
Figure 3
ig n
BNSF TAIL TRAC K
ALASKAN WAY SEAWALL
MARION STREET
PEDESTRIAN BRIDGE
D es
1000
SENECA ST OFF-RAMP
00
2 25+
00
Harbor Steps
S e ct
g ic
o lo
Ge
ig n
5 + 53
D es o n 2 2
ti
a
t
S
COLUMBIA ST ON-RAMP
ic
l og
eo
n G 8+38
2
s ig
n 2
De
ti o
S ta
00
BNSF TUNNEL
23
5+
00
De
24
0+
00
24
5+
00
De
s ig
Buildings and structures that were evaluated and locations of design geologic sections
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第十五屆大地工程學術研究討論會論文集(Geotech2013)
Proceedings of the 15th Conference on Current Researches
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中華民國 102 年 9 月 11-13 日, 雲林, 台灣
September 11-13, 2013
Yunlin, Taiwan
approximately 0.001% based on in situ dynamic testing
(shear wave velocity measurements). The anticipated
level of shear strain from tunneling for static analysis is
approximately 0.35 percent (Mair 1993). The maximum
shear modulus was reduced to a shear modulus
appropriate for a shear strain of 0.35% based on the
representative modulus reduction curve(s) for the
modeled soil units, and the soil was modeled as a linear
elastic-plastic material.
Limited modeling performed using non-linear soil
moduli indicated that using representative, constant soil
moduli yielded similar or more conservative results.
Thus, using a representative, constant soil modulus was
deemed an acceptable simplification for static liner
design.
Foundations. Shallow foundations were modeled as
pressures at model boundaries (e.g., at the bottom of
basement excavations). For deep foundations, a
sensitivity analysis was performed, modeling the deep
foundations using forces applied within the model grid
versus modeling structural elements interfaced to the soil
mesh. While using structural elements can produce more
accurate load distributions, it requires more modeling
effort and assumptions. The sensitivity analysis showed
that for a structure on piles, the differences in soil loads
on the liner between the two methods were negligible.
Thus, the simplified force method was used for the liner
design.
Grout. Sensitivity analyses performed using
estimated grout properties resulted in significantly
reduced soil loads on the liner compared to modeling the
grout with properties similar to the adjacent soil. The
grout filling the gap between the outside diameter of the
liner and the excavation was conservatively modeled
based on the strength and stiffness of the adjacent soil.
Modeling in 2-D. Most of the geotechnical
numerical modeling for the liner design was performed
using 2-D FLAC. While a 2-D geotechnical model
cannot explicitly account for the various contributions to
volume loss and ground relaxation due to tunnel
construction, the bulk of the modeling was performed in
2-D to efficiently evaluate the design cases using
simplifying, conservative assumptions regarding ground
relaxation as described below in “Excavation relaxation.”
Limited 3-D modeling was performed at critical design
sections and compared favorably with the 2-D model
results.
Excavation Relaxation. The soil loads on the liner
are dependent on the volume loss and the resulting soil
relaxation/arching that occurs due to tunnel excavation
and construction. The excavation relaxation was modeled
in 2-D by reducing in situ stresses at the perimeter of the
tunnel excavation and monitoring the volume loss at the
tunnel level (i.e., percentage volume/foot of contraction
relative to the excavation volume/foot).
The final volume loss at the tunnel level was
conservatively assumed to be equal to the empirically
estimated volume loss at the ground surface. In shallow
sections and where normally consolidated soil constitutes
a significant thickness of the overburden, the final
volume loss at the tunnel level and at the ground surface
will likely be similar. However, in deeper sections and
5.1 SCREENING ANALYSIS
An elastic evaluation of the influence on soil
stresses at the elevation of the tunnel crown was
performed to determine which groups of structures
warranted more detailed analysis using numerical
modeling. The structures were first organized according
to their associated design geologic section because the
elastic evaluation was used to determine which structural
influence cases were numerically modeled based on the
design geologic sections chosen to represent the
variability in geologic and hydrogeologic conditions. The
structures were then grouped based on those buildings
that line up along sections perpendicular to the tunnel
alignment.
The elastic evaluation considered the following
factors when estimating the influence of a structure on
the stresses at the tunnel liner crown.
1.
Unloading due to soil excavation for
underground openings (i.e., tunnels, basements).
2.
Loading due to the estimated bearing
pressure of the structure.
3.
Foundation depth – deep foundation loads
assumed to act at the bottom of the deep foundation
elevation over the area of the foundation.
4.
Height and offset of structure loading from
tunnel crown.
5.2 GEOTECHNICAL MODELING
Two-dimensional (2-D) numerical modeling was
used to determine the final design static soil loads and
static soil springs for use in the structural design of the
tunnel liner (see Figure 4). Unfactored structural liner
reactions were also determined from the geotechnical
models. This geotechnical modeling was performed
using the computer code FLAC Version 6.00 (Itasca
2011).
Figure 4
Example geotechnical model
5.2.1 SIMPLIFYING ASSUMPTIONS
Several conservative, simplifying assumptions were
made to increase modeling efficiency and check the
minimum liner design criteria. If these assumptions
resulted in issues for the minimum liner design,
additional effort was focused on refining the evaluations
at these critical design sections.
Soil Modulus. The maximum shear moduli (see
Table 2) are reported for a shear strain level of
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第十五屆大地工程學術研究討論會論文集(Geotech2013)
Proceedings of the 15th Conference on Current Researches
in Geotechnical Engineering in Taiwan
中華民國 102 年 9 月 11-13 日, 雲林, 台灣
September 11-13, 2013
Yunlin, Taiwan
because some volume loss and soil relaxation/arching
occurs before installing the liner. This was accounted for
by first relaxing the tunnel excavation consistent with
target volume loss at the tunnel level, then generating the
soil springs by increasing/decreasing the model forces at
the perimeter of the excavation and monitoring
displacements. As previously discussed, the geotechnical
models use a linear modulus; however, the soil springs
generated are non-linear due to plasticity effects. Figure
6 shows an example of radial soil springs demonstrating
the non-linear nature due to plasticity, as well as the
non-symmetric soil spring response for displacement
toward, versus away from, the center of the tunnel (note
that positive deformation is toward the center of the
tunnel in Figure 6).
where overconsolidated soil constitutes a significant
thickness of the overburden, the final volume loss at the
tunnel level will be greater than at the ground surface as
a result of bulking/dilation and arching. Since soil loads
on the liner will decrease due to arching as volume loss
increases, assuming a lower volume loss was
conservative.
For deep sections, preliminary models assuming the
final volume loss at the tunnel level was the same as the
volume loss empirically estimated at the ground surface,
which was as low as 0.2%, yielded an equivalent
overburden soil load as high as 4.3 tunnel diameters.
This high soil load appeared to be overly conservative
when compared to closed-form solutions and typical
equivalent overburden loads for tunnels (i.e., less than
2.5 tunnel diameters). For select deep sections, 3-D
modeling of the full tunnel excavation and construction
procedures was performed to provide a better estimate of
the final volume loss at the tunnel level.
The design values of final volume loss at the tunnel
level used in the 2-D geotechnical models generally
ranged from approximately 0.5% in deeper sections to
1% in shallower sections.
5.2.2 SOIL LOADS
The estimated soil loads ranged from an equivalent
overburden of approximately 0.2 tunnel diameters in
very shallow sections to 2.0 tunnel diameters in deep
sections. Groundwater pressures at the tunnel invert
varied from 0.1 to 5.2 bars. The 335 kPa (7,000 psf)
future building surcharge case often resulted in higher
soil loads on the liner than the existing buildings and
structures cases, and the increase in loads was
particularly significant for shallower sections (see
Figure 5).
Figure 6
section
Example radial soil springs for shallow
5.2.4 STRUCTURAL REACTIONS
Liner structural reactions from the geotechnical and
structural models were compared to ensure the models
yielded similar results for unfactored loads, and the
models were found to be in good agreement. Based on
this assessment, the liner reactions from the geotechnical
models were provided to the structural engineer to
review which cases were critical for structural design and
warranted the more detailed evaluation using seismic and
structural models. This step limited the geotechnical
modeling and post-processing effort required to generate
the soil springs, as well as limiting the cases that needed
to be evaluated in the structural design models.
In general, the 335 kPa (7,000 psf) future building
surcharge case yielded the highest moments and axial
loads in the liner for the geotechnical models. Figures 7
and 8 show the liner bending moment and axial loads for
deep sections and the 335 kPa (7,000 psf) future building
surcharge case. Note these liner reactions are reported
per foot length of tunnel and based on unfactored loads
from the geotechnical model.
Figure 5 Example soil and groundwater loads on liner
for shallow section
5.2.3 SOIL SPRINGS
The soil springs generated for use in the structural
engineering models were also dependent on volume loss
8
第十五屆大地工程學術研究討論會論文集(Geotech2013)
Proceedings of the 15th Conference on Current Researches
in Geotechnical Engineering in Taiwan
中華民國 102 年 9 月 11-13 日, 雲林, 台灣
September 11-13, 2013
Yunlin, Taiwan
solution in Figure 9 shows a similar load distribution
around the tunnel. However, the magnitude of the soil
loads for these two methods differ somewhat, which is
essentially dependent on the Terzaghi arching
formulation and the modeled soil relaxation. In general,
soil loads estimated from the geotechnical models were
higher for very deep sections (e.g., 252+13 in Figure 9)
and lower for very shallow sections. These comparisons
indicated the geotechnical model loads were more
conservative, because the geotechnical modeled soil
loads yielded higher axial loads in the deep sections
where axial load governs liner design and lower axial
loads (and reduced moment capacity) in the shallow
sections where moment governs liner design.
Figure 7
sections
Structural liner moment reaction in deep
Figure 9 Comparison of geotechnical model and
closed form solution soil loads
Figure 8
sections
Structural liner axial thrust reaction in deep
5.2.6 SENSITIVITY ANALYSIS
Sensitivity analysis was performed to evaluate the
potential effects of encountering highly sheared or
slickensided soils in ESU 7, and varying lateral earth
pressures of the glacially overridden soil.
These
conservative checks were not critical for the liner design
relative to the envelope of loading conditions along the
alignment.
Load Resistance Factor Design (LRFD)
evaluations performed by the structural engineer for
strength limit states indicated the liner load demands
were near but below the axial thrust capacity for the
highest loads developed in deep sections based on the
minimum liner design criteria (i.e., 0.6 m (2 ft) thick, 1%
steel reinforcement). In the shallowest section with the
smallest axial thrust loading, the liner load demands were
near but below the moment capacity for the minimum
liner design criteria.
5.2.5
COMPARISON TO
FORM SOLUTION
6 SEISMIC ANALYSIS
While the focus of this paper is the static
geotechnical analysis, a brief description of the seismic
analysis is included for completeness. Analysis of the
bored tunnel included loads from seismic deformations
and ground accelerations considering three primary
modes of deformation during seismic ground movement:
(1) ovaling, (2) axial, and (3) curvature deformations.
A two-step analysis procedure similar to the static
analysis was adopted to analyze seismic ovaling. First,
deformations of the soil surrounding the liner due to the
seismic wave propagating from bedrock through soil
media, without the liner, were computed with a
continuum model. Second, the ground deformations were
imposed on the liner through supporting elements
(non-linear springs) using beam-on-spring models by
performing non-linear dynamic time history analysis.
The liner was analyzed for three Expected Earthquake
CLOSED-
Select geotechnical modeling soil loads on the liner
were compared to the Einstein and Schwartz (1979)
closed-form solution soil loads for the no-slip case based
on the Terzaghi arching formulation (ITA 2000) to
estimate input soil stresses. For comparisons to the
Einstein and Schwartz (1979) closed-form solution, the
results from the geotechnical models with the smallest
loading/unloading were used to limit the influence from
existing structures on the comparisons. Example
comparisons are presented on Figure 9.
The comparisons of the geotechnical model soil
loads to the Einstein and Schwartz (1979) closed-form
9
第十五屆大地工程學術研究討論會論文集(Geotech2013)
Proceedings of the 15th Conference on Current Researches
in Geotechnical Engineering in Taiwan
中華民國 102 年 9 月 11-13 日, 雲林, 台灣
September 11-13, 2013
Yunlin, Taiwan
events and three Rare Earthquake events, and the results
for each event were enveloped for design.
was the lead structural engineer for liner design.
Intecsa (Spain) provided 3-D FLAC analysis for
verifying the ground loss at the tunnel level, as wells as
nonlinear soil modulus modeling. Earth Mechanics, Inc.
performed the geotechnical seismic liner design analysis.
Hart Crowser staff who helped prepare this manuscript
include: Eric Lindquist, Mary Gutierrez, Rebecca
Ramsey, and Sue Enzi.
7 CONCLUSIONS
Geotechnical analyses for the SR 99 Bored Tunnel
static liner design were performed to efficiently meet the
contract requirements, check the minimum liner design
criteria, and focus seismic and structural design effort on
critical design sections. Elastic screening analyses were
used to limit the geotechnical numerical modeling
needed to address the influence of existing structures on
the liner. Geotechnical modeling incorporated several
simplifying assumptions to efficiently evaluate geologic
variability and the influence of existing and future
structures, including using representative, constant soil
moduli; modeling existing foundations using applied
loads rather than interfaced structural elements;
modeling the grout injected around the liner using the
properties of the adjacent soil; modeling the tunnel
excavation and liner installation in 2-D; and using
conservative values for volume loss. Both static soil
loads and springs for structural modeling were generated
in the geotechnical models accounting for the volume
loss that occurs prior to installation of the liner. For static
liner design the future building surcharge contract
requirement generally yielded the highest soil loads and
structural liner reactions. Comparison to closed-form
solution results indicated the geotechnical models
yielded similar or more conservative soil loads.
Sensitivity analysis of potential zones of pre-existing
sheared/slickensided clays and varying lateral earth
pressure coefficients performed at select locations did
not yield critical design cases relative to the envelope of
loading conditions along the alignment.
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Booth, D.B. (1991). “Glacier Physics of the Puget Lobe,
Southwest Cordilleran Ice Sheet,” Geographie
physique et Quaternaire, Vol. 45, No. 3, pp. 301-315.
Einstein, H.H. and Schwartz, C.W. (1979). “Simplified
Analysis for Tunnel Supports,” Journal of the
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Galster, R.W., and Laprade, W.T. (1991). “Geology of
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Seattle Tunnel Partners (STP) (2011). SR 99 Bored Tunnel
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Seattle Tunnel Partners (STP) (2012). SR 99 Tunnel
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ACKNOWLEDGEMENT
The authors would like to acknowledge
collaboration throughout the design process with the
project owner, Washington State Department of
Transportation; the design-build contractor, Seattle
Tunnel Partners, and the prime designer, HNTB
Corporation. Dr. Yang Jiang of HNTB Corporation
10