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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

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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

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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%=

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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

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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-----=

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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.)

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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

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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=~

~

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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

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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

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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.

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Figure 11. Support Category IV interaction diagramverification analyses for SEE