T. CurtinW, R. Adey and F. Andreassen^ · circular section 7.583 feet in internal diameter (Figure 1). The segments are 6 !4 inches thick and 42 inches long. In developed

Forensic investigation of failed precast concrete

tunnel segments through field performance

monitoring and boundary elements analysis

T. CurtinW, R. Adey and F. Andreassen^

(**Computational Mechanics Inc. Billerica, MA, USA

Email: [email protected]*Computational Mechanics BEASY, Southampton, UK.Email: [email protected]̂verdup Corporation, New York, NY, USA

Abstract

A comprehensive study of the structural integrity of a precast concrete tunnel wasconducted following the discovery of cracking, during construction, in somesections of the tunnel liner. The structural behavior of the jointed tunnel ring wasinvestigated through experimental testing and computer simulation. Data gatheredfrom field performance monitoring and full-scale laboratory testing was used inconjunction with numerical simulation to investigate the effect of stressconcentrations at bolt pocket recesses and excessive rotation at jointed connections.A commercially available Boundary Element code was chosen to simulate thedistressed behavior of the tunnel liner. Computer models were developed tosimulate the complex interaction at the jointed connections in the tunnel ring and toinvestigate crack propagation in tunnel segments subject to axial load.

1 Introduction

A forensic investigation was conducted to determine the cause of cracking inprecast concrete segments used to construct jointed rings that formed a tunnel. Thefirst 1800 feet of tunnel alignment was characterized by frequent cracking in thecrown and invert. Distress in the segments was characterized by both longitudinalcracks, that appeared to initiate from localized recesses in the segments, anddiagonal cracks at bolt pocket used to fasten the segments together. Approximately15 % of the segments in this stretch of tunnel exhibited some degree of distress.

Transactions on Modelling and Simulation vol 22, © 1999 WIT Press, www.witpress.com, ISSN 1743-355X

276 Boundary Element Technology

These cracks, originally formed during construction of the tunnel, later continued toopen as the surrounding ground stress became active on the tunnel.

The type and extent of cracking was not easily explained following review ofdesign documents describing the anticipated performance of the tunnel rings. Inorder to determine factors responsible for the failed segments, a multifacetedprogram was implemented to investigate the structural integrity of the tunnel liner.This program included field performance monitoring, full-scale experimentaltesting, and numerical simulation.

As part of the field performance monitoring evaluation, several tunnel rings wereheavily instrumented with strain gages to measure both longitudinal andcircumferential stress. The jacking force exerted on the tunnel rings was measuredusing pressure transducers. This field performance monitoring data wassupplemented by a full-scale laboratory test of a tunnel ring where the applied stressand boundary conditions where carefully controlled to evaluate sensitivity of tunnelring deformation to various lateral support conditions.

In conjunction with field performance monitoring and experimental testing,numerical modeling was used to simulate tunnel ring deformation and explorepotential failure mechanisms. The commercially available boundary element code,BEASY, was selected for creation and analysis of computer models intended toevaluate stress distribution in the segments, analyze complex interaction at jointedconnections, and determine probable fracture propagation paths.

2 Description of Tunnel Liner

The tunnel liner is comprised of six precast concrete segments which form acircular section 7.583 feet in internal diameter (Figure 1). The segments are 6 !4inches thick and 42 inches long. In developed view the segments appear astrapezoids symmetrical about the longitudinal axis of the segment. A 2-inchdiameter grout hole is located at the center of each segment.

The segments are bolted together at two locations along each transverse matingsurface (cross joint) and at one location along each ring mating surface (ring joint).Bent steel plate inserts provide holes and faying surfaces for bolting. Formedrecesses or "pockets" provide access to bolt holes. All mating surfaces are providedwith neoprene gaskets and compression packing. The ring orientation is such thatcross joints are located at the 12, 2, 4, 6, 8, and 10 o'clock positions. The wide andnarrow faces of the trapezoidal segments line up at the ring joints.

Reinforcement is located on the outside face of each segment in the direction ofthe circumferential stress. The reinforcement consists of four No. 4 bars persegment plus D5 deformed wire at 5-inch centers. No reinforcement was specifiedfor the inside face of the segments.


Boundary Element Technology 277

Figure 1. Segmented tunnel liner assembled at casting yard to verify geometrictolerancing.

3 Observed Structural Distress

The pattern of longitudinal and diagonal bolt pocket cracking is shownschematically in Figure 2. The observed longitudinal cracks were typically singlehairline cracks, but crack widths of 0.0625 to 0.125 inches were also observed.These cracks were most common at the 1 and 11 o'clock positions. Thelongitudinal cracks typically started (or ended) at a bolt pocket and passed throughthe grout port (Figure 3). The cracks were observed to be at least as deep as theback face of the bolt pocket (approx. 3 inches). The cracks were typically cleanfractures, oriented normal to the segment, and absent of significant spallingsuggesting a tension crack.

Diagonal cracking and occasional spalling around bolt pockets was common atthe crown and invert cross joints although it was also observed less frequently at the2 and 10 o'clock joints. The cracking was generally clean and ranged from hairlineto 0.125 inch in width. The diagonal cracks typically occurred near the bent plateradii and extended toward the bolt pocket intersecting approximately midway alongthe recess forming the long bolt pocket, and at the filleted ends of the short boltpocket recess.


DIRECTION OF TUNNEL HEADING

Diagonal Bolt Pocket Cracks

Inward Deflection of Segment Corner

Figure 2. Plan view schematic showing generalized crack locations in precastconcrete tunnel ring segments.

Figure 3. Photograph showing longitudinal crack in tunnel ring segment.

4 Approach to Forensic Investigation

Based on field observations of the distressed tunnel segments and review of designdocuments an attempt was made to characterize likely failure mechanisms anddevelop a forensic program to address the likelihood and impact of thesemechanisms. It was speculated that bolt pocket cracking was caused by excessivejoint rotation due to lack of adequate passive resistance at the tunnel springline.However the actual mechanism responsible for the cracking was not clearly defined.The cause for longitudinal cracking on the inside face of the segments was notreadily explainable. Given that the segments were designed to carry negativebending moment due to an eccentricity inherent in the cross joint design and the fact



that a negative bending moment would create compression on the inside face of thesegment it was difficult to explain the tensile cracks.

The scope of the forensic program, based on the probable failure mechanismsdescribed above, is as follows:

1. Assess in situ structural behavior of tunnel rings with regard to constructionand earth loading through a comprehensive instrumentation program.

2. Conduct a full scale load test of tunnel ring to assess effect of lateral support(and thus increased joint rotation) on tunnel deformation.

3. Perform numerical modeling to investigate contributing factors responsible fortunnel ring distress. The contributing factors were addressed through thefollowing computer simulations:

(a) Two-dimensional segmented ring under different loadingconfigurations

(b) Three-dimensional model of bolted cross joint with contactloading

(c) Three-dimensional model of single segment under axial load(d) Crack growth in a segment.

4.1 Field Performance Monitoring

Select tunnel rings were instrumented with strain gages to measure longitudinal andcircumferential strain and evaluate the impact of both construction and earthloading. The strain gages used were specifically designed for direct embedment inconcrete and were installed during the casting of the segment. Of the six gages ineach segment two were positioned to measure longitudinal strain and four werepositioned to measure circumferential strain. The strain gages were arranged attwelve 30 degree increments around the ring. The longitudinal gages werepositioned at approximately the mid-thickness of the segment and thecircumferential gages were installed 2 inches from the inner and outer facesrespectively.

The longitudinal jack force was measured using pressure transducers installedon each manifold T connected to the TBM's hydraulic system. Signal wires fromthe strain gages and pressure transducers were routed to a data acquisition systemwhich was programmed to read the sensors at predefined intervals. The data wasautomatically reduced using custom designed software to produce a graphicaldisplay of longitudinal and circumferential strain distribution in the tunnel ring.

4.2 Load Test Program

A full scale load test was conducted to investigate tunnel ring behavior under loadfor different boundary conditions. The load test assembly is shown in Figure 4 andconsisted of a pair of rings assembled and bolted together. The rings were setvertically in a sand box extending over a base area covering a 120 degree angle. A12-inch thick layer of sand, for load distribution, was located at the invert. The load



was imposed on the top of the test ring assembly via an upper sandbox extendedover an area covering a 120 degree central angle. The sand cover at the crown wasabout 12-inches thick for load distribution. Lateral restraints were provided by two1.5 inch diameter tie rods. The reaction developed in the tie rods was distributedvia steel strongbacks over an area covering a 50 degree central angle, 25 degreesabove and below the springline.

30 1-inch steel plate: Rubber Bearing Pad4-inch Stiffener Coupling

Load Cell^̂'-v0.5-inch dia Tie Rod

II I W Stongbackŷ

ANCHORAGE DETAIL

Figure 4. Schematic showing load test assembly.

The test was conducted for four different boundary conditions which consistedof varying degrees of slackness in the tie rod assembly (simulating different degreesof support at the tunnel springline). The load was increased incrementally until amaximum pressure of 1350 psf was applied. This load is well below the design loadand is equivalent to a free standing soil prism of about 11.25 feet. The load wasimposed by the sand layer and a number of one inch thick steel plates placed on thetop of the sand.

After each load increment, diameter changes, joint openings, tie rod reactionforce, and crack openings were measured. Diagonal cracking was observed at thebolt pockets during the test however no structural cracking through the center of theany segment was observed during the load test suggesting that the longitudinalcracks were not generated by excessive bending moment.

4.3 Numerical Simulation

Computer models were generated using MSC/PATRAN as the pre- andpostprocessor and the BEASY-PATRAN Interface for control of the boundaryelement modeling and analysis environment. Models were analyzed using the



BEASY Mechanical Design and Fatigue and Crack Growth software. Theboundary element method incorporated in the BEASY software provides a powerfulmodeling system where the behavior of detailed structural features can beaccurately simulated. These modeling advantages are partially rooted in the robustcontact and fracture mechanics algorithms utilized in the computer code.

An accurate contact analysis was crucial to evaluate the stress and deformation atthe cross joint. The BEASY non linear contact algorithm benefits from the directlycomputed tractions and displacements on the contact surfaces. The contactalgorithm uses a self-adaptive solution scheme where the load increments arepredefined and adjusted automatically depending on the rate of solutionconvergence. For each load step the solution is computed using an iterativeprocedure until the compatibility and equilibrium conditions are satisfied. Theconstraint based contact algorithm automatically enforces the surface contactconditions predicting the position of the contact surfaces and the resulting stressdistribution on the contact surface.

The impact of fracture on the structural integrity of the segment was animportant concern and accurate simulation was promising using the fracturemechanics algorithms incorporated in the BEASY fracture code. Two notablefeatures include the use of discontinuous elements to predict stress intensity factorsat crack tips, and the use of the Dual Boundary Element Method (DBEM) to solvecrack propagation problems.

Discontinuous elements allow the stress field to become discontinuous betweenelements and thus are very useful for modeling the rapidly changing stress field at acrack tip. A discontinuous element is defined as an element where the nodes (orsolution points) are not located at the mesh points used to define the geometry butrather within the area of the element. The DBEM is based on the application of thedisplacement boundary integral equation on one of the crack surfaces and thetraction boundary integral equation on the other. In this way mixed mode crackgrowth problems can be solved in a single region domain. The method is wellsuited to handle crack propagation problems and provides fully automatic re-meshing of the crack surface.

4.3.1 Segmented Tunnel Ring ModelThe segmented tunnel ring model was developed to evaluate ring deformations withrespect to the integrated performance of the cross joints (Figure 5). The tunnel ringwas modeled using distinct zones to define the segments, and the different materialproperties representing concrete and reinforcing steel. The actual cross sectionalprofile of the cross joint was modeled, including the gasket groove, and the reliefgrooves at the extreme ends of the segment. By using a boundary element methodfor this analysis it was possible to build a realistic model of the cross joint.

The cross joint was modeled by applying appropriate boundary conditions at thezone interface representing the mating surface. The bolt prestress was originallysimulated using a "lack of fit" condition applied over a washer diameter of 1.5inches. A "lack of fit" of-0.000042 inches (equivalent to a bolt prestress of 1930psi) was computed assuming the bolt strain occurred over the thickness (0.625inches) of the connected bent plates. The bolt prestress was based on the valuespecified in the design documents.



Contact boundary conditionon joint mating surface

condition at bolt connection

Figure 5. Boundary element model of upper section of segmented ring. Notedetailed modeling of each joint using contact and lack-of-fit boundary conditions.Bent plate and reinforcing steel modeled in each segment.

Over the remainder of the cross joint mating surface a contact boundarycondition with a zero initial gap was defined in both the normal and tangentialdirections. A frictionless condition was assumed considering that little slippage atthe joint was expected given the bolted connection. The model was analyzedassuming a state of plane stress.

After several trial runs it was found that that this approach resulted in an"overstiff' joint where the reported deflections were much less than those measuredin the load test. The cross joint boundary conditions were revised so that the "lackof fit" condition was applied only over the bolt diameter (0.875 inch) whicheffectively allowed more rotation at the joint. Following this modification thecomputer model results more closely matched the load test results. It can beassumed that this is a more realistic approach since the washer is a flexiblecomponent and most likely would deform around the bolt head reducing the actualload transmission near the outer diameter of the washer

4.3.1.1 Load Case 1 - Full Scale Load Test Simulation Load Case 1 wasintended to simulate the loading used in the full scale load test. This step wasnecessary to assess the accuracy of the computer model. A 1350 psf load wasuniformly distributed over an area covering a 120 degree central angle, 60 degreeseach side of the crown cross joint. The reaction at the base was assumed equal to amodulus of subgrade reaction for a very dense sand (800 kef). A spring stiffness of463 psi/in, uniformly distributed over an area in the invert covering a central angleequal to 120 degrees, was used to model the invert reaction. The lateral support wasmodeled using a spring boundary condition distributed over an area covering a 50



degree central angle on each side of the springline. A spring stiffness equivalent tothe modulus of subgrade reaction of 219 psi/in was used.

The results of the computer simulation compared favorably with the load testdata in terms of the horizontal ring displacement and relative joint openingdirections. A maximum horizontal diameter of 0.08 inch was predicted. This isapproximately 55% less than the deflection of 0.18 inches measured at maximumload during the load test. Although joint rotations predicted by the computer modeloccurred in directions similar to that observed during the load test, the magnitude ofopening tended to be less. Figure 6 illustrates the simulated opening of a jointlocated at the 10 o'clock position.

The difference between computer model and experimental results can beattributed to the slightly nonlinear behavior of the test ring after cracks formedaround the bolt pockets. This cracking was not simulated in the computer modelbut would be expected to make the ring behave in more flexible manner. Althoughnot evaluated as part of this project it is likely that the computer model resultswould compare more favorably at lower loads where true linear elastic behaviorwould be expected in the test ring.

Figure 6. Deformed shape of tunnel ring cross joint. Note contact analysis allowssimulation of joint opening. Bolt prestress simulated using "lack of fit" boundarycondition.

4.3.1.2 Load Case 2 - Outward Radial Ring Displacement Load Case 2 wasused to evaluate the performance of the tunnel ring within the tailskin of the TBM.It was based on applying a uniform outward radial displacement on the insidesurface of the ring. The outward radial displacement (0.002967 inches) wascomputed based on an average applied jack thrust of 500 psi and a plane stresscondition. The intent of Load Case 2 was to determine the magnitude anddistribution of circumferential tensile stress in an unconfmed ring when subject toan axial load. The circumferential stress in the concrete predicted by the computermodel ranged from 200-300 psi at the mid-length of the segment remote from thecross joint.



The average measured circumferetial tensile stress in an uncracked instrumentedtunnel ring during loading within the tailskin of the TBM was approximately 200psi. The corresponding average longitudinal stress was approximately 325 psi(average jack thrust was approximately 28 kips). The measured circumferential andlongitudinal stress distribution for this particular instrumented ring are illustrated inFigure 7. It should be noted that the measured longitudinal strain data was notuniform around the ring. This non-uniformity is most likely attributed to theeccentricity between the jack shoe and the segment bearing area in addition to thefact that only 10 out of the 12 jacks were active during this particular shove.

,598 psi

239 psi

,216 psi

432 psi

465 psi

LONGITUDINAL STRESS

[ \ Thmst Jack Off

Thrust Jack On

CIRCUMFERENTIAL STRESS

Figure 7. Longitudinal and circumferential stress distribution measured in tunnelring while unconfmed in tailskin of TBM and subject to axial jack pressure.

4.3.2 Longitudinal Crack Simulation ModelA slightly modified model of a single tunnel segment was created to determine if,and in what direction, longitudinal cracks would grow from the bolt pockets andgrout port. A uniform traction of 1000 psi was applied at two locations along thewide end of the segment to represent the load from two thrust jack pads. Crackswere located at locations of high principal stress determined from a stress analysisof a three-dimensional model of the segment. Cracks, assumed 0.1 inch in length,were located in the fillet at the short bolt pocket recess and on opposite sides of thegrout port hole in directions parallel to the long axis of the segment.

A crack growth simulation was performed using 30 crack propagation steps. Thecrack growth distance for each step was 0.2 inches. The crack located at the filletwas the dominant crack and propagated a distance of approximately 6 inches beforethe analysis was stopped. This was considered sufficient to demonstrate the crackgrowth path for the given loading and allow comparison to field observations ofactual longitudinal cracking in the segments.



The stress intensity factors (SIF) were calculated using the J Integral method andthe crack growth direction was computed using the maximum principal stresscriterion. This criterion postulates that the growth of the crack will occur in adirection perpendicular to the maximum principal stress at the crack tip.

The simulated crack growth path, shown in Figure 8, shows excellent agreementwith the actual longitudinal cracking observed in the segments. The crack, near thefillet in the small bolt pocket, was characterized by a significantly greater stressintensity factor (SIF) when compared to the two cracks located at the grout port.The maximum SIF calculated at the crack tip was approximately 830 psi in whichis sufficient to initiate cracking considering that the fracture toughness KC forconcrete is reported to range from 200-1300 psi in ( Hertzberg 1989).

It should be noted that this analysis was based on linear elastic fracturemechanics. The authors acknowledge that there is some non linear behavior at thecrack tips in concrete and that the softening behavior of the material in the fracturezone plays an important role in the fracture process. Interested readers can find adetailed discussion of the application of boundary element analysis for crack growthin concrete in the work by Saleh (1997).

Li

•tetacJWo'"

Figure 8. Deformed shape showing crack propagation path.

4.3.3 Bolted Cross Joint ModelA three-dimensional computer model of a cross joint was developed to provideexplanation for the cracking observed at the bolt pockets. The model consists oftwo 30 degree segment sections joined together at the cross joint. One of the 30degree segment sections includes the actual bent plate bolting surfaces and thereinforcing bars. The boundary element mesh for this section is shown in Figure 9.The connecting 30 degree segment does not contain any reinforcing steel and wasconstructed primarily to provide an appropriate contact reaction at the joint matingsurface. The contact reaction at the mating surface was achieved by restraining thissegment section from movement in the three global coordinate directions andassuming a stiffness of sufficient magnitude to simulate a rigid piece.



The mating surface of the cross joint was defined with a zone interface where theinterface conditions were similar to those used for the two dimensional analysis (i.e.bolt prestress simulated using a "lack of fit" boundary condition, contact loadingused on mating surface). The load was applied to the segment containing thereinforcing steel using the ultimate stress design load for a location 30 degrees fromthe crown joint as specified in the design documents. The stress on the inner surfaceof the segment was -1641 psi (compression) and varied linearly to a value of 362 psiat the outer surface. This loading represents a temporary condition on the tunnelwhere full overburden loading is considered without hydrostatic pressure (i.e.dewatered state).

Figure 9. Boundary element mesh for segment section showing detailed of boltedconnection and reinforcing steel embedded in concrete.

Results from this model provided useful insight into the behavior of the boltedcross joint and associated cracking. The deformed shape accurately simulates theopening of the joint on the inside face and indicates that there was significantflexure in the bent plates bolted together at the cross joint. This flexure is mostpronounced near the curved radii of the bent plates and generates significant tensilestress in the adjacent concrete (Figure 10). The high tensile stress (above modulusof rupture) extend approximately 2-3 inches toward the rear of the bolt pocketrecess. High tensile stress were also predicted at the fillet corners of the small boltpocket.

5 Conclusion

Longitudinal cracking on the inside face of the segment can be best explainedthrough a combination of mechanisms that were acting during construction of thetunnel ring. Field performance monitoring and computer simulation strongly



suggest that cracking is primarily a result of stress concentrations created by boltpocket and grout port recesses in the segment. The stress concentration effect isexacerbated by outward radial deformation (and associated circumferential tensilestress field) of the tunnel ring during axial loading within the tailskin of the TBM.This is a construction related loading that would not have easily been accounted forduring the design phase because the main design focus was on checking that thesegments would not fail in axial compression.

Zones of high

tensile stress

rfSC/PATRAN Version 7.5 03- Feb-9911:05:56>eftmn: TJC,3DJOINTJAN18nod, Displacements, Transladonal - Max Principal, (NON-LAYERED)

Bolted connection

Figure 10. Deformed shape of a single bent plate.

Measured strain data and jack thrust pressure support the occurrence oflongitudinal cracking through the mechanisms discussed above. Although themeasured longitudinal stresses were less than the allowable design loads somesegments still failed, not through excessive bearing, but rather through the creationof tensile cracks.

As originally thought, the primary factor in the diagonal bolt pocket crackingappears to be the flexing of the bent plate at the cross joints during joint rotation.Flexing of the bolt pocket plates imposed a "diagonal tension" on the concretebetween the bolt pockets and the flange of the bent plate. This condition wasmagnified with increased joint rotation. As a consequence of increased jointrotation the acute angle corner of the segment tends to deflect inward.Measurements from the load test indicated that under extreme conditions (full slackcondition) support this occurrence. This behavior was also observed in thedistressed portion of the tunnel where the acute angle of the segment at the 2o'clock position rotated and deflected inward with respect to the adjacent segment.



The behavior observed in the field and demonstrated during the load test was alsoaccurately simulated in the three-dimensional model of the cross joint.

The investigative approach used for this project was successful in determiningreasonable explanation for the various modes of cracking observed in the tunnelsegment. The numerical models served as a useful tool to supplement fieldmeasurements and allowed engineers to assess a variety of potential failuremechanisms quickly and accurately. The ability to quickly alter computer modelsand create a number of "what-if' scenarios is fundamental to performing asuccessful forensic study. The BEASY suite of software provided the wide range ofanalysis capability needed to perform a structural integrity study of this magnitude.

References

Saleh, A.L., 1997, Crack Growth in Concrete using Boundary Elements, Topics inEngineering, Vol. 30, Computational Mechanics Publications, Southampton UK andBoston, MA ,176pp.

Anderson, T.L. 1995, Fracture Mechanics Fundamentals and Application 2 ed.CRC Press Boca Raton, Florida, 688 pp.

Niku, S.M., Adey, R.A, and Baynham, J., 1989, "Contact Analysis using BEASY:Theory and Application, 11* International Conference on Boundary ElementMethods, Boston 1989, CM Publications

Branson, D.E. and Trost, H., 1982, "Unified Procedures for Predicting theDeflection and Centroidal Axis Location of Partially Cracked Nonpresetressed andPrestressed Concrete Members", ACI Journal March April 1982, p119-130.

Odman, S.T.A., 1973, Analysis of Stresses in Cracked Reinforced Concrete Beam,Handlingar Proceeding NR44, Swedish Cement and Concrete Research Institute atthe Royal Institute of Technology, Stockholm , Sweden, ppl-54.

BEASY Crack Growth Guidebook (version 5.0), June 1994, ComputationalMechanics BEASY Ltd, Ashurst Lodge, Ashurst, Southampton

Aliabadi, M.H. and Rooke, D.P., 1991, Numerical Fracture Mechanics,Computational Mechanics Publications/Kluwer Academic Publishers. 280 pp.

Hertzberg, Richard W., 1989, Deformation and Fracture Mechanics of EngineeringMaterials, 3"* edition, John Wiley and Sons, New York, NY, 680 pp.


Documents

T. CurtinW, R. Adey and F. Andreassen^ · circular section 7.583 feet in internal diameter (Figure 1). The segments are 6 !4 inches thick and 42 inches long. In developed