-
417
Design Analyses for a Large-Span Tunnel in Weak Rock Subject to
Strong Seismic Shaking
Bhaskar B. ThapaJacobs Associates, San Francisco,
CaliforniaJohannes Van GreunenJacobs Associates, San Francisco,
CaliforniaYiming SunJacobs Associates, San Francisco,
CaliforniaMichael T. McRaeJacobs Associates, San Francisco,
CaliforniaHubert LawEarth Mechanics Incorporated, Los Angeles,
California
ABSTRACT: The proposed Caldecott fourth bore will consist of a
two lane highway tunnel along Califor-nia State Route 24 near the
City of Oakland. The proposed design and construction sequence for
the 15-m-diameter tunnel are based on the New Austrian Tunneling
Method (NATM). The initial support system incor-porates
combinations of shotcrete, rock dowels, lattice girders, spiles,
and grouted steel pipe canopies. Thefinal lining is cast-in-place
reinforced concrete. A waterproofing membrane and drainage system
are placedbetween the initial and final linings. State Route 24 is
a lifeline route, required to be open to emergency vehi-cles within
72 hours after a major earthquake, defined as having a return
period of 1,500 years and a peakground acceleration of 1.2 g.
Although the seismic design criteria are stringent, the design of
the tunnel liningsystem is ultimately controlled by static ground
loads in the weak rock along the alignment.
INTRODUCTION
Project BackgroundThe existing Caldecott Tunnel complex
includesthree bores along State Route 24 (SR 24) throughthe
Berkeley Hills in Oakland, California. The Cali-fornia Department
of Transportation (Caltrans) andthe Contra Costa Transportation
Authority (CCTA)propose to address congestion on SR 24 near
theexisting Caldecott Tunnels by constructing a fourthtunnel that
will provide two additional traffic lanes.The proposed
horseshoe-shaped fourth bore is1,036 m (3,399 ft) long, 15 m (50
ft) in diameter,and 9.7 m (32 ft) high. The project will include
shortsections of cut-and cover tunnel at each portal,
sevencross-passageway tunnels between the fourth boreand the
existing third bore, electrical substationbuildings, and a new
operations and control build-ing. State Route 24, considered a
lifeline route byCaltrans, is required to be open to emergency
vehi-cles 72 hours after an earthquake with a returnperiod of 1,500
years and a peak ground accelerationof 1.2 g. Construction of the
fourth bore is antici-pated to begin in the summer of 2009 and be
com-pleted in 2014.
GEOLOGY
Major Geologic Formations and StructureThe geology of the
alignment is characterized bynorthwest-striking, steeply-dipping,
and locallyoverturned marine and non-marine sedimentaryrocks of the
Middle to Late Miocene age. The west-ern end of the alignment
traverses marine shale andsandstone of the Sobrante Formation. The
SobranteFormation includes the First Shale, Portal Sand-stone, and
Shaly Sandstone geologic units as identi-fied by Page (1950). The
middle section of thealignment traverses chert, shale, and
sandstone ofthe Claremont Formation. The Claremont
Formationincludes the Preliminary Chert, Second Sandstone,and
Claremont Chert and Shale geologic units(Page, 1950). The eastern
end of the alignmenttraverses non-marine claystone, siltstone,
sandstone,and conglomerate of the Orinda Formation. Majorformations
and geologic units within these forma-tions are shown Figure 1.
The geological structure of the project area hasbeen
characterized as part of the western, locallyoverturned limb of a
broad northwest-trending syn-cline, the axis of which lies east of
the project area.The fourth bore alignment will encounter four
major
-
418
inactive faults, which occur at the contacts betweengeologic
units. These faults strike northwesterly andperpendicular to the
tunnel alignment. In addition tothe major faults, many other zones
of weak groundwill be encountered, such as smaller-scale
faults,shears, and crushed zones.
West of the fault contact between the Prelimi-nary Chert and
Shale and the Second Sandstone, thebedding encountered in the
fourth bore generallydips predominantly northeast. East of this
fault con-tact, the bedding dips southwest. Several joint setsoccur
within each geologic unit, and random jointsoccur in almost all
orientations in all geologic units.Intrusive sandstone dikes and
hydrothermally-altered diabase dikes occur most frequently in
theClaremont Chert and Shale, but may be encounteredless frequently
in other geologic units.
The structure of the rock mass units along thealignment varies
from blocky in the best ground todisintegrated or crushed in the
poorest-qualityrock. Average RQD ranges from 5 to 81. RockMass
Ratings (Bieniawski, 1989) and Q values(Barton, 1988) at the tunnel
scale vary from 20 to65, and 0.006 and 10.5, respectively. Rock
strengthvaries from weak to moderate along the alignment.Average
values of measured unconfined compres-sive strength in the various
geologic units varyfrom 5.2 MPa (750 psi) to 21.6 MPa (3190
psi).Mudstone, siltstone, and shale in the Orinda andClaremont
Formations are expected to exhibitswelling behavior. The fourth
bore has been classi-fied as a gassy tunnel by the California
Occupa-tional Safety and Health Administration.
SeismicityThe San Francisco Bay Region is considered one ofthe
more seismically active regions of the world,based on its record of
historical earthquakes and itsposition astride the tectonic
boundary between theNorth American and Pacific plates. During the
past160 years, faults within this plate boundary zonehave produced
numerous small-magnitude (M6) earthquakes. Major faultsthat
comprise the 80-km-wide plate boundary in theSan Francisco Bay
Region include the San Gregorio,San Andreas, Hayward, and Calaveras
Faults.
The active Hayward Fault, located 1.4 km(0.9 mi) west of the
Caldecott Tunnel, is the closestmajor fault to the project site,
capable of producing amagnitude 7.4 earthquake. The southern
segment ofthe Hayward Fault produced the 1868 Haywardearthquake of
estimated magnitude 6.8 that wasaccompanied by 30 to 35 km (19 to
22 mi) of sur-face faulting.
INITIAL SUPPORT DESIGN The initial support system design is
based on theSequential Excavation Method (SEM), also knownas the
New Austrian Tunneling Method (NATM).NATM provides the required
flexibility to accom-modate the variable ground conditions and
weak,folded, and faulted rock that will be encounteredalong the
Caldecott fourth bore alignment. Thedesign approach involves
classification of groundalong the alignment into several ground
classes,development of corresponding support categories,
Figure 1. Geologic formations and geologic units
-
419
and definition of criteria for application of the sup-port
categories during construction. Four major andtwo minor ground
classes, and corresponding sup-port categories, have been developed
for construc-tion of the fourth bore. Support category I applies
tothe best quality rock mass and Support Category IVapplies to the
poorest quality rock mass. For thefourth bore design, the team also
developed addi-tional support measures to be used if
unexpectedgeologic conditions are encountered during con-struction
or monitoring reveals unexpected, unfavor-able ground behavior. A
description of the generaldesign approach is provided in Thapa et
al. (2007)and is not repeated here. However, the sectionsbelow
describe some of the specific design analysesincluding both two-
and three-dimensional conver-gence-confinement analyses that were
performedwith FLAC (Itasca, 2005) to evaluate specific designissues
for the NATM initial support design. Thesedesign issues are:
Stress relaxation ahead of the tunnel heading Face stability
Lining loading across weak zones
Stress Relaxation Ahead of the FaceFLAC3D models of the full
NATM excavation andsupport operation were developed for each
supportcategory to estimate the amount of relaxation in theground
ahead of tunnel face. The FLAC3D modelsexplicitly represent the
sloping core used for facesupport and spiling presupport. The
shotcrete lining
is modeled using Mohr-Coulomb elastic-plastic con-tinuum
elements in FLAC3D. The hardening of theshotcrete lining is modeled
as the tunnel top headingand two bench cuts advance at prescribed
rates andlags to represent the early age creep effects of
shot-crete described in Thapa et al. (2007).
Ground relaxation factors are estimated basedon a tunnel
longitudinal displacement profile(LDP) and a ground reaction curve
(GRC). Thetunnel LDP (see Figure 2) demonstrates the devel-opment
of tunnel radial displacement as a functionof distance along the
length of the excavation, andcan be generated from FLAC3D analysis
results.The GRC (see Figure 3) shows the tunnel radialdisplacements
as a function of support pressure,and can be generated from a
two-dimensionalFLAC analysis.
To estimate the ground relaxation factor, aFLAC3D analysis of
the entire excavation sequencewas performed. From this analysis,
three LDPswere generated, one corresponding to each stage
ofexcavation. From each LDP, the drift radial displace-ment (ur0)
prior to installation of initial support wasestimated. Then, a
FLAC2D analysis was performedto generate the GRC for the excavation
stage underconsideration. Next, the radial displacement
(ur0)estimated from the LDP was used to locate the cor-responding
support pressure on the GRC. Theground relaxation factor (GRF) for
the drift underconsideration was estimated as follows:
Figure 2. Longitudinal displacement profiles for SC I
GRF 1 R( ) 100%=
-
420
The GRFs for other stages of tunnel excavationwere estimated in
the same way. Figure 4 illustratesschematically the use of the LDP
and GRC to esti-mate the ground relaxation factor ahead of the
tunnelface. The radial displacements utilized in generatingthe LDPs
and the GRCs are the vertical displacementsnear the crown of the
top-heading drift and the
horizontal displacements near the springline of thebench drifts.
The above approach used in estimatingthe GRF is consistent in
principle with the currentpractice in tunnel design
(Carranza-Torres andFairhurst, 2000 and Graziani et al., 2005).
Tunnel displacements (or strains defined as theradial
displacements divided by the tunnel radius)
Figure 3. Ground reaction curves for SC I
Figure 4. Schematic illustration of estimation of ground
relaxation factor using FLAC3D results
-
421
calculated from FLAC3D and FLAC2D are gener-ally in good
agreement. Iterative calibration of theGRF ensures that the
displacements or tunnel strainof the supported tunnel from FLAC3D
at the sectionwhere a plane-strain condition is reached matchthose
from FLAC2D. GRF estimates from the aboveanalyses ranged from 58%
to 65% for various sup-port categories.
Face StabilityFLAC3D was also used to evaluate face stability
bydetermining the factor of safety (F) against globalshear failure
for the top heading drift. In theFLAC3D face stability analysis, F
is the factor bywhich the rock mass shear strength must be
dividedto bring the drift face to the verge of failure.
Theresulting factor of safety (F) is the ratio of the actualrock
mass shear strength to the reduced shearstrength at failure, which
can be expressed as:
where, o is the actual shear strength and r is thereduced shear
strength at incipient failure.
Figure 5 shows the actual and reduced rockmass strength
envelopes for Support Category I, cor-responding to various factors
of safety. The strengthenvelopes shown in Figure 5 are based on
fourHoek-Brown failure criterion strength parameters.The four
Hoek-Brown criterion parameters for eachfactor of safety were
determined using a cubic splineinterpolation scheme built into
Microsoft Excel.
The procedure for calculation of the face stabil-ity factor of
safety begins with initialization of themodel to top heading
equilibrium conditions follow-ing excavation and support
installation using theactual rock mass strength envelope. Factors
of safetyfor the face region are then calculated by
iterativelyreducing the rock mass strength (corresponding
toincreasing factors of safety), flagging failure
zonescorresponding to the iteration factor of safety andcontouring
zones with the same factor of safety (seeFigure 6). This iteration
is repeated until the modelfails to reach mechanical equilibrium or
a predeter-mined number of increments in the F value isreached. The
range of F values evaluated varies from1.0 to 5.0. During
iteration, failure of a zone repre-senting the rock mass is defined
as the non-conver-gence of the zone velocity to a value of less
than 106m/s. Face stability is evaluated in a region thatextends to
four tunnel diameters longitudinally and tothe model limits
vertically and transversely. Predictedfactors of safety against
general shear failure for thetop heading drift ranged from 3.2 in
Support CategoryI without any face support to 1.3 in Support
CategoryIII with a sloping core for face support.
Lining Loading Across Weak ZonesA 180-m-long reach adjacent to
the fault contactbetween the Second Sandstone and Claremont
Chertand Shale geologic units is expected to have sub-reaches of
varying ground quality ranging from verypoor to fair. This reach
occurs under the highest coveralong the tunnel alignment. Shotcrete
lining thicknessrequirements for this reach were evaluated
usingFLAC3D to account for the effect of longitudinal
Figure 5. Strength envelopes for various factors of safety in
Support Category I
For-----=
-
422
arching on lining loads. Figure 7 shows the liningloads
developed across this reach from a FLAC3Danalysis. Comparison of
FLAC3D results to aFLAC2D analysis that does not account for
longitudi-nal arching shows that lining loads computed usingFLAC3D
are about 30% lower than the loads calcu-lated using a plane-strain
FLAC2D analysis. It isnoted that the FLAC3D results are in general
agree-ment with the FLAC2D results in other reaches withuniform
ground conditions.
FINAL LINING AND SEISMIC DESIGN
Final Lining SystemThe Caldecott fourth bore uses a double
lining sys-tem consisting of an initial support system (dis-cussed
above) and a cast-in-place reinforcedconcrete final lining (Figure
8). A waterproofingmembrane with a geotextile backing layer for
drain-age will be installed between the initial support andthe
final lining. The initial support system is
Figure 6. Factor of safety around face of top heading in Support
Category I (Figure shows longitudinal section through tunnel
centerline. Top heading half-width =7.5 m, height=5.5 m.)
Figure 7. Stresses in shotcrete lining through ground with
varying material properties (Tunnel width=15.0 m, height=10.5
m.)
-
423
designed to carry the ground loads that develop dur-ing
construction, while the cast-in-place reinforcedconcrete final
lining is designed to carry long-termground loads and any
additional loads resulting fromfinishes or anchored equipment. The
final lining willalso accommodate seismic deformations and pro-vide
a durable and sound tunnel lining.
General descriptions of loads and load combi-nations, ground
loads, and seismic demands havebeen described in Thapa et al.
(2007) and are notrepeated here. The following key aspects of the
finallining design are discussed below:
Load sharing between the initial and finallinings
Wave scattering analysis Pseudo-static time history analysis of
seismic
demands
Ground Loads from Load SharingThe initial shotcrete lining and
the final concrete lin-ing will behave as a combined lining system.
Thelong-term performance of the system will dependnot only on the
final lining, but also on the long-termload-carrying capability and
the durability of the ini-tial shotcrete lining. During
construction, the initialsupport will carry the ground load.
However, twoessential components of the initial support, the
rockdowels and the shotcrete lining itself, are expectedto
deteriorate with time. The rock dowels proposedfor the project are
not protected against corrosion
and are considered temporary. In most of the tunnel,the first 50
mm (2 in.) of shotcrete lining are appliedas a flash-coat and
considered sacrificial. In the FirstShale reach of the Sobrante
Formation, the first100 mm (4 in.) of shotcrete is considered
sacrificialbecause of the high sulfate concentration in
thegroundwater in this reach. The remaining shotcretelayers are
also expected to deteriorate to somedegree over time. In addition,
the initial shotcretelining is assumed to have no flexural capacity
due topossible deterioration of any reinforcing embeddedtherein.
Thus, as these components deteriorate overtime, the final lining
will support a significant por-tion of the ground load.
Analyses were performed to assess the effect ofthe degradation
of the initial support and to deter-mine the part of the ground
load that will be trans-ferred to the final lining. Analyses were
performedusing FLAC 5.0 (Itasca, 2004). Key assumptions ofthe
analyses were:
Rock dowels were completely deteriorated. Initial shotcrete
lining thickness reduced by
neglecting the sacrificial layer as describedabove.
The modulus of the reduced shotcrete liningwas degraded to 60%
of its original designvalue.
The initial shotcrete lining has no flexuralcapacity after
degradation.
Due to the presence of the waterproofing mem-brane, the
interaction between the initial and
Figure 8. Final lining
-
424
final linings was modeled with stiff radialsprings and no
tangential springs.
The analysis was performed using two methods:
Method A: The full tunnel excavation was mod-eled in one step
with both the degraded initiallining and the final lining in place.
This is a con-servative assumption that would be expected
totransfer a somewhat higher portion of the groundload to the
stiffer final lining.
Method B: The excavation and initial supportinstallation
sequence was modeled to developthe forces in the initial support.
Thereafter theinstallation of the final lining and deteriorationof
the initial support were modeled. Simplychanging the properties of
the shotcrete liningwhen the lining-ground system is in
equilib-rium is not a viable analytical approach usingFLAC. Nodal
forces are still in balance and noredistribution of forces would
occur. Therefore,to force the model to perform a meaningfulsolution
cycle, the forces (thrusts, shears, andmoments) in the shotcrete
lining were changedat the same time as the shotcrete lining
proper-ties. The forces in the shotcrete lining werereduced by the
same factor used for the degra-dation of the material properties,
thereby limit-ing the ground load supported by the initiallining
and forcing redistribution of loads. Theshotcrete lining forces
change during cycling,and therefore have to be updated after
eachcycle to make sure that the resulting forcesalways satisfy the
following criterion:
where: p represents the new parameters (thrust,shear, and
moment); po corresponds to the originalparameters; f is the
reduction factor, = (1 percentdegradation ) = 0.6 here.
The results of both analyses with Method A andB indicate that
the final lining will attract a maxi-mum of 50% of the ground load
supported by theinitial lining. The final lining was
conservativelydesigned to support 2 3 of the ground load
supportedby the initial lining.
Wave Scattering AnalysisWave scattering analyses were performed
to calcu-late ground deformations around the tunnel openingin
response to seismic wave propagation. This analy-sis accounts for
the effect of local conditions such astunnel geometry, adjacent
tunnel cavities, geology,topography, and variation in rock quality.
The timehistory of ground distortions around the tunnel
obtained from wave scattering analyses were used asinput for the
pseudo-static analysis of the tunnelfinal lining seismic demand (as
described later inthis paper).
The scattering analysis was performed usingelastic material
models with properties adjusted forsmall strain dynamic conditions.
At large shearstrains modulus reduction and increased dampingwere
considered in the analysis. The tunnel liningwas not included in
the models as the linings are sig-nificantly more flexible than the
ground and, there-fore, only the properties of the ground determine
thedeformation of the tunnel opening.
The scattering analyses were performed usingQUAD4M, a finite
element computer program(EMI, 2007). The finite element models
include atransmitting boundary capable of minimizing seis-mic wave
reflection at the finite element boundary,which is used to model a
semi-infinite space outsidethe finite element domain (Hudson et
al., 1994)(Lysmer and Kuhlemeyer, 1969). Three transversecross
sections of the mined tunnel, a cut-and-covercross section at the
west portal, and a longitudinalsection of the tunnel were evaluated
for wave scat-tering effects. The three transverse cross
sectionswere selected to represent the critical combinationsof
cover and ground properties along the fourth borealignment.
Since the project is part of a lifeline route,ground motion
criteria consistent with other impor-tant facilities on the same
route including the Beni-cia-Martinez bridge, San FranciscoOakland
Baybridge (SFOBB) and Yerba Buena Island (YBI) tun-nel, were
selected for design. Thus, the groundmotion adopted for the Safety
Evaluation Earth-quake (SEE) and Functional Evaluation
Earthquake(FEE) are the 1,500 and 300 year return period uni-form
hazard spectra respectively. The performancerequirements for the
SEE are that the fourth borewill be open to emergency vehicle
traffic within 72hours following an SEE. Performance
requirementsfor the FEE are that the fourth bore remains
fullyoperational and experiences minimal, if any, dam-age. Three
sets of earthquake time histories weredeveloped to spectrum match
the reference SEErock spectra; Figure 9 shows three component
timehistories of the SEE reference rock motion for oneof the three
sets of earthquake time series used in thedesign.
Results of the scattering analyses are illustratedin Figure 10
showing a comparison of the intensityof the computed motions at the
tunnel perimeter andthe reference motion in terms of
accelerationresponse spectra. The spreading of the responsespectra
clearly indicates non-coherent wave propa-gation, which results in
differential motion aroundthe tunnel cavity. The computed
acceleration time
p f po=~
~
-
425
histories at the nodes around the tunnel perimeterwere
integrated twice to yield displacement time his-tories which served
as the multiple-support inputmotions to the tunnel lining
Pseudo-Static Time History Analysis of Seismic Demand
ApproachState-of-the-art beam-spring and beam-continuummodels
were used to perform pseudo-static time his-tory analyses of the
tunnel final lining using multi-ple-support displacement time
histories from thescattering analyses described above. Two types
ofnumerical models were used to calculate liningstrains, stresses,
and forces: two-dimensionalSAP2000 (CSI, 2006) beam-spring models
withnonlinear support springs (gap elements) to modelground
behavior, and two-dimensional beam-contin-uum models using both
FLAC (ITASCA, 2005) andADINA (ADINA R&D Inc.) with elastic
continuum
elements to model ground behavior. The two-dimen-sional
beam-spring models were used for design tocalculate strains,
stresses, and forces in the fourthbore lining and cut-and-cover
structures, and toensure that the results were within acceptable
stressand ductility limits. The two-dimensional beam-con-tinuum
models were used to verify the resultsobtained from the beam-spring
models. All of thenumerical models were initialized with gravity
loads(rock loads and rock wedge loads) before the simu-lation of
the seismic events.
Two-dimensional beam-spring SAP2000 (CSI,2006) models of the
final lining were developed forall support categories. The lining
was represented bylinear beam elements while the ground was
modeledwith equivalent springs, considered to be compres-sion-only
to simulate the passive support the groundwill provide to the
lining. The stiffness of the springswas based on the spring
tributary area and theground modulus of elasticity. The static mean
modu-lus of elasticity was used for all analyses of static
Figure 9. Reference rock motion (SEE Set 1) for the Caldecott
fourth bore
-
426
loads. For seismic analyses the dynamic modulus ofelasticity was
determined by increasing the staticmoduli by a factor of between
two and three.
Gravity loads were applied through the supportsprings by
displacing the fixed ends of the springsand then iterating to
achieve structural equilibriumwith the required load in each of the
support springs.The pseudo-static time history analyses were
per-formed by imposing displacements, calculated ateach time step
through the scattering analysesdescribed above, to the final
lining.
ResultsThe results of the analyses indicate that a 381-mm(15-in)
final lining with 35 MPa (5,000 psi) concretecan support the ground
loads and accommodate theseismic deformations. The final lining
thickness wasselected for constructability and is controlled by
thethrust resulting from ground loads in the high coversection of
Support Category III. In general, the anal-yses indicated that the
maximum bending momentin the final lining, as calculated with the
differentmodels, are not sensitive to the modulus of theground.
However, the lining thrust was generallysignificantly higher for
cases using the upper boundmodulus of elasticity.
Figure 11 summarizes the maximum liningthrust and moment for one
of the critical support cat-egories using the upper-bound ground
modulus. Inthis support category, the thrust and bendingmoments due
to seismic deformations result in some
excursions outside the interaction envelope. How-ever, the
calculated reinforcing steel stresses andconcrete strains are well
within the allowable limits.
CONCLUSIONSDesign of initial support required several
three-dimensional evaluations. These evaluations wereperformed
using FLAC3D and the results were com-bined with traditional
two-dimensional and closed-form-solution analyses. The FLAC3D
evaluation ofrelaxation ahead of the face justified the use of
highrelaxation factors which resulted in lower supportloading, and
contributed to the selection of morerealistic support requirements.
FLAC3D evalua-tions of face stability showed that typical
closed-form solution evaluations can be unconservative andthat
three dimensional numerical analyses helpassess more realistic face
support requirements. TheFLAC3D evaluation of lining loading across
weakzones was unique and key to evaluation of supportrequirements
in high cover reaches. The FLAC3Devaluation in weak zones showed
the proposed shot-crete lining thickness was sufficient and the
thickerlining required by a two-dimensional analysis wasnot
necessary.
State-of-the-art seismic design analyses wereperformed on this
project due to the critical lifelineclassification of the facility.
The design consideredhigh levels of shaking, several ground motion
timehistories for each design event, non-coherence dueto wave
scattering, and pseudo-static time historyanalysis of the lining
response. The analyses showedthat the low cover portal sections of
the tunnel weresubject to more severe seismic demands than
interiorsections with high cover. The design analyses dem-onstrated
that a 381-mm (15-in) final lining with35 MPa (5,000 psi) concrete
can support the groundloads and accommodate the seismic
deformations.Seismic demands do not control the thickness of
thefinal lining, despite the close proximity of theproject to a
major active fault and seismic design cri-teria corresponding to an
earthquake with a1,500-year return period and a peak ground
acceler-ation of 1.2g.
ACKOWLEDGMENTSThe authors would like to acknowledge
GeomatrixConsultants for their work on the site geology,
ILFConsultants for independent reviews of the initialsupport
designs, and SC Solutions for their work onseismic demand
analysis.
The contents of this paper were reviewed by theState of
California, Business, Transportation andHousing Agency, Department
of Transportation and
Figure 10. Response spectra at fourth bore tunnel opening for
Station 107+60 under SEE Set 1 motion
-
427
the Contra Costa Transportation Authority. The con-tents of the
paper reflect the views of the authorswho are responsible for the
facts and accuracy of thedata presented herein. The contents do not
necessar-ily reflect the official views or policies of the State
ofCalifornia or the Contra Costa TransportationAuthority. This
paper does not constitute a standard,specification or
regulation.
REFERENCES Page, B.M. (1950), Geology of the Broadway Tun-
nel, Berkeley Hills, California, Economic Geol-ogy, Vo. 45,
No.2
John, Max and Mattle, Bruno. Shotcrete LiningDesign: Factors of
Influence. 2003 RETCProceedings.
I t a sca Consu l t ing Group Inc . , 2005 , Fas tLagrangian
Analysis of Continua (FLAC) Ver-sion 5.0, Minneapolis.
Hashash, YMA et al., Seismic Design and Analysisof Underground
Structures, Tunneling and Under-ground Space Technology 16 (2001)
pp. 247293,Elsevier.
Hudson, M., Idriss, I. M. and Beikae, M. (1994),Users Manual for
QUAD4M, A Computer pro-gram to Evaluate the Seismic Response of
SoilStructures Using Finite Element Procedure andIncorporating a
Compliant Base, Department ofCivil & Environmental Engineering,
University ofCalifornia, Davis.
Lysmer, J. M. and Kuhlemeyer, R. L (1969), FiniteDynamic Model
for Infinite Media, J. of theEngineering Mechanics Division, ASCE,
Vol. 95,No. EM4, August, pp 859877.
SAP2000 Version 10, Computers and Structures Inc,Berkeley,
California, 2006
ADINA, ADINA R&D, Watertown, MassachusettsEarth Mechanics
Incorporated, Caldecott Improve-
ment Project, Technical Memorandum No. 16:Results of Scattering
Analyses, 2007
Bieniawski, Z.T. (1989), Engineering Rock MassClassifications,
Wiley, New York
Barton, N., 1988, Rock Mass Classification and Tun-nel
Reinforcement Selection Using The Q-system,Rock Classification
System for Engineering Pur-pose, ASTM Special Publication 984,
AmericanSociety for Testing Materials, Page 5988.
Thapa, B.B. et al. (2007) Preliminary Design of theCaldecott
Fourth Bore, Proceedings of the RapidExcavation and Tunneling
Conference, Toronto.
Carranza-Torres, C. and Fairhurst, C., 2000. Appli-cation of the
Convergence-Confinement Methodof Tunnel Design to Rock Masses That
Satisfy theHoek-Brown Failure Criterion. Tunneling andUnderground
Space Technology, Vol. 15, No. 2,pp. 187213.
Graziani, A., Boldini, D., and Ribacchi, R. 2005.Practical
Estimate of Deformations and StressRelief Factors for Deep Tunnels
Supported byShotcrete. Rock Mechanics and Rock Engineer-ing, 38
(5), 345372.
Figure 11. Support Category IV interaction diagramverification
analyses for SEE