structural analysis of post-tensioned concrete containment building repair using 3-d finite elements

7/23/2019 Structural Analysis of Post-Tensioned Concrete Containment Building Repair Using 3-d Finite Elements

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Structural Analysis of Post-Tensioned Concrete Containment

Building Repair using 3-d Finite Elements

Authors:

Peter R. Barrett, P.E., Computer Aided Engineering Associates Inc., 60 Middle QuarterMall, Woodbury, CT 06798, (203) 263-4606,[email protected]

Daniel B Fisher Jr. P.E., AREVA Group, 7207 IBM Drive, Charlotte, N.C. 28262

ABSTRACT

The most efficient method of replacement of major internal components such as steamgenerators in nuclear power plants may require the creation of a construction opening inthe side of the containment building. For repairing post-tensioned concrete containment

buildings, a major design challenge is to develop the most efficient scheme for tendon de-

tensioning and subsequent re-tensioning. Stresses and displacements must be monitoredin the containment wall and liner throughout the repair sequence. Nonlinear finite

element analysis using the ANSYS general analysis package can be used to simulate the

entire construction process and thus assure an adequate design margin of safety at allstages.

Recent developments in computer CPU speed and RAM advancements have made it

possible to perform complex nonlinear Finite Element Analysis (FEA) on an entirecontainment building overnight on a desktop machine. The nonlinear analysis techniquediscussed in this paper includes explicit modeling of the tendons and concrete including

the tendon-concrete load interaction. Tendon tensioning and de-tensioning is modeled

using an initial strain approach where link elements are coupled to the containment

building wall. The wall is modeled with 3-D brick elements. Element birth and death isused to simulate the process of cutting the construction opening and subsequent patching

of the wall in a stress-free state. This modeling method is critical to capture the local

bending response in the patch that is often neglected in simplified models. This paperpresents the details while illustrating the importance of explicitly modeling the

construction and hole-patch-wall interaction.

INTRODUCTION

Replacing steam generators requires material and personnel access to the interior of the

reactor building. Development of the temporary construction access must show that:

1. There will be no damage to the containment building at any time during theconstruction work on an opening.


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2. Creating an opening in the wall of the containment building and patching the

concrete does not change the structural integrity of the building.Structural analysis of the post-tensioned concrete containment building repair using the

finite element method provides an accurate and efficient means of evaluating these

criteria. The analysis input to meet these requirements includes:

Modeling a symmetric portion of the building (typically 180 degrees or less)

Modeling the hoop and vertical tendons explicitly.

If necessary modeling the equipment hatch area and evaluating its contribution to thebuildings overall state of stress.

Developing a geometrically parametric model of the construction opening so that itcan be adjusted to variable sizes to meet design criteria.

Developing the ability to remove individual tendons (hoop or vertical).

Developing the ability to vary an individual tendons force (hoop or vertical)

Including the effects of tendon loss for both vertical and horizontal tendons.

Each of these capabilities is illustrated in the body of this paper through the exampleanalysis of a representative containment building. The results presented are typical of

what might occur in an actual evaluation, but are not specific to any real structure.

FINITE ELEMENT MODEL DEVELOPMENT

In constructing a finite element model there is always the trade off betweencomputational accuracy and computational time to solve. As computers get faster, we are

able to build models that provide a better understanding of the physical response the

building under goes during the repair operations. The independent modeling of theconcrete, tendons, and patch interface will result in more accurate design evaluations.

The following element types and there applications are explained in more detail:

1. 3-d brick elements to model the concrete building

2. 1-d truss elements to model the tendons

3. Spring elements to connect the patch to the building4.

Surface-to-surface contact elements to simulate the repair boundary

between the patch and existing wall

Containment Wall - 3-d Brick Elements

Brick elements are used to model the containment wall since they can predict a nonlinear

through thickness stress distribution that cannot be captured using conventional shellmodeling. The brick elements will also predict the incompatibility of the stress free patch

and the pre-loaded building nonlinear deformation pattern. A large through-thickness

bending stress distribution is most prevalent at the patch after tendon re-tensioning.Mesh density studies show that six elements through the thickness are adequate to

capture this response and still preserve a model that can be easily solved on a desktop

computer. The liner plate is conservatively ignored in the demonstration model, althoughit could easily be added in the form of shell elements on the inside face of the


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containment building. Brick elements are aligned with the tendons such that the tendon

(truss) elements line-up with the containment (brick) concrete elements. Thesecoincident nodes allow for direct coupling between the concrete and tendon elements.

Figure 1 illustrates a 180-degree model. The patch region is illustrated in a different

color since the material properties will change after the hole is replaced with the patch.

The size and shape of the patch is defined as user-friendly parametric input in theanalysis file to automate the process of performing design iterations. The abutments are

also explicitly modeled with bricks to capture their eccentric stiffness and provide tendon

attachment points.

FIGURE 1-FINITE ELEMENT MODEL OF CONTAINMENT BUILDING

1-d Truss Tendon Elements

Truss elements are used to model the vertical and hoop tendons to provide flexibility in

evaluating variations in tendon loads (de-tensioning and re-tensioning) during the repairdesign process. Truss element nodes are defined at coincident locations of the brick

elements where load transfer is required between tendons and the containment wall.

Rigid beam elements are used at the abutments (connecting the ends of the tendons to thecontainment wall) to distribute the tendon support loads to the concrete elements since

the anchorages are not modeled explicitly. Coupling in the radial direction between the

tendon elements and the containment wall is used to transfer load between the hoop

tendons and the containment wall. Other degrees of freedom of the tendons not requiredare fixed to prevent rigid body motion. An initial strain is used to define the tendon

forces. Forces are derived directly from the stresses and tendon areas. Each element isgiven a different initial strain that is a function of the tendon loads and losses. Tendon

strains (forces) are calculated from a scripted input file such that all tendon loads can be

changed with a single variable. The tendon loads are defined using ANSYS APDL

scripts that compute the actual tendon load from its geometric position taking into


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account the distance from the abutment and radius of curvature. The tendon losses are

computed based on the following equation:

This tendon loss is programmed directly into the truss elements such that the exact tendonforces are calculated correctly at each position in the model. In areas where the tendons

overlap, two sets of tendons are tied to the same nodes. Tendons are smeared togetherwhere applicable to simplify the finite element model. Vertical tendons only transfer

load between the tendon and containment wall at the anchorages and where the tendon

slots are not straight. At locations of curvature the tendon normal loads are applied to thecontainment building via radial couples. By modeling the tendons independently, tendon

forces can easily be increased or decreased to evaluate different tensioning and de-

tensioning scenarios. Figure 2 illustrates sample vertical and hoop tendons on a sectionof the wall adjacent to the hole/patch.

FIGURE 2-HOOP AND VERTICAL TENDONS

The equation for remaining force is:

( )SKJL

ePP +

=

Where

LP = Load at a location along the tendon after losses are

accounted for

JP = Load at the jacking point

= Curvature friction coefficient

= Total angle change, radians

K = Wobble friction coefficient per foot

S = Length of tendon straight portion


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1-d Spring Elements

In the boundaries around the patch, spring elements are used to form a continuous bondbetween the containment wall and future patch region, prior to the patch being cut. The

use of independent nodes for the patch wall along the cut line allows for the subsequent

modeling of the opening and patching loading sequence. The spring elements are definedwith large spring stiffnesses during the initial analysis steps where the building is

modeled prior to the opening being cut and subsequent de-tensioning. After the hole is

cut, the springs are kept at a large stiffness to restrict rigid body motion of the killedelements in the hole. Upon patching and engaging of the contact elements, the spring

elements are reduced to a very low stiffness to allow any relative motion to occurbetween the patch and wall that is not constrained by the contact elements.

Surface-to-Surface Contact Elements

Surface-to-surface contact elements are used to simulate the repaired boundary between

the patch and existing wall such that a loss of bond can be simulated. The contact

elements are killed during the initial stages of the analysis where the previously describedsprings hold the original wall in-place. Contact elements are activated after the patch is

birthed to transmit compressive and shear loads (based on a defined friction

coefficient), and yet not allow tensile forces to develop between the patch and

surrounding concrete wall. Friction is used to simulate the effects of the concrete to resistshear loads at the edges of the patch.

LOADING SEQUENCE

Since the analysis of the construction sequence is nonlinear and path dependent, it is

necessary for the analysis to follow the construction sequence. Each load step is scripted

to define changes where applicable in tendon loads, material properties, gravity loads,and patch interface elements. A sample loading sequence is summarized as follows:

! LS 1: Dead Load + Tendon Loads + Equipment Loading! LS 2: Dead + Tendons + Equipment + Accident

! LS 3: Dead + Tendons + Equipment

! LS 4: Tendons de-tensioned in hole only - vertical and horizontal! LS 5: Tendons de-tensioned locally away from the hole

! LS 6: Create the hole in the wall

! LS 7: Remaining vertical tendons detensioned as necessary! LS 8: Patch installed stress free

! LS 9: Patch installed and contact elements activated! LS 10: Springs removed! LS 11: Partially re-tension verticals tendons

! LS 12: Partially re-tension hoop tendons

! LS 13: Fully re-tension hoop and vertical tendons! LS 14: Fully re-tensioned hoop and vertical tendons + Accident


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The loading sequence defined above was automated using scripts in ANSYS. For each

load step, stress, force and displacement data can be extracted from the finite elementmodel and processed to determine the adequacy of the building to support the defined

loading. The analyses are nonlinear since element birth and death is used to create the

hole and replace the concrete in a stress free state. The contact elements also require an

iterative solution. By developing a user-friendly automated sequence, the analysis modelcan be used as a design tool to determine the most efficient size of opening and pattern of

tendon de-tensioning and subsequent re-tensioning. The input script can be run by a

designer without the need of being an analysis expert.

ANALYSIS RESULTS

Since the analysis of the construction sequence is nonlinear and path dependent, it is

necessary for the analysis to follow the construction sequence explicitly. Sequential

loading allows for post-processing the analysis results in form of history plots that trackthe concrete forces and displacements. Results from selective load steps are provided to

demonstrate the effects of explicitily modeling the repair on the nominal buildingstresses.

Figure 3 illustrates the hoop and vertical stresses under tendon and dead loads prior to the

repair. By modeling the abutments explicitly, the stress concentrations are captured in

this area. For all the contour plots illustrated in this report, the blue regions representcompression, while the red areas represent tensile stresses. For all the containment

building figures, the same contour scales are used so the colors are consistent between

plots.

FIGURE 3HOOP AND VERTICAL STRESS UNDER TENDON AND DEAD LOADS

Variations in hoop tendon forces extracted from the first load step are illustrated in Figure

4. The red colors illustrate the maximum tendon loads at the abutments. Tendons lossesin the example simulation result in a 14% reduction from the tendon attachment points to

the mid-plane abutment pass through.


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FIGURE 4HOOP TENDON FORCE DISTRBUTION

Figure 5 illustrates equivalent vertical and hoop forces after the tendons in the hole region

have been either removed or reduced in tension. The blue color represents either aremoved or reduced tendon load. The removed tendons have a reduced pre-load and a

reduced cross-section to eliminate their stiffness from the model. The variation in hoop

tendon forces (colors) is caused by the difference in equivalent tendon forces caused by

variations in mesh/tendon spacing.

FIGURE 5TENDON FORCES AFTER REMOVAL IN THE HOLE REGION


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Hoop and vertical stress distribution in the containment wall after the opening has been

cut are shown in Figure 6. The reduced hoop stresses circumferentially away from thehole are a result of the tendon de-tensioning in this area. Away from the hole, the

compressive stress state illustrated with the blue colors is maintained and is nearly

identical to the pre-repair state illustrated in Figure 3. Vertical compressive stresses are

highest in the local region inside the opening where the load path has to transition aroundthe hole.

FIGURE 6HOOP AND VERTICAL STRESS DISTRIBUTIONS AFTER HOLE CUT

Figure 7 illustrates the hoop and vertical stress distribution in the containment wall after

the opening has been repaired and the tendons re-tensioned. The hoop compressivestresses return to the entire wall. Local bending stresses are developed in the patch that

results in tensile forces on the inside surface of the wall that typically requires additional

reinforcement.

FIGURE 7HOOP AND VERTICAL STRESS DISTRIBUTIONS AFTER REPAIR AND RE-TENSIONING

If the analysis is performed without including the hole and subsequent re-patch, the stress

distributions around the patch will not be captured correctly and could result in an under


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design of the patch reinforcement. Figure 8 illustrates the hoop and vertical stresses

predicted when the final loading environment is applied directly to the model withoutincluding the path dependent cutting and repairing of the hole.

FIGURE 8HOOP AND VERTICAL STRESS DISTRIBUTIONS WITHOUT PATH DEPENDENT LOADING

When comparing hoop stresses between Figures 7 and 8 (the figures on the left), noticethe light blue region in and around the patch. This indicates a reduction in hoop stress in

the patch region caused by the repair sequence that would not be predicted without

simulating the construction sequence. To overcome this reduction, higher tendon re-

tensioning is often required. Similarly if one compares the vertical stresses in the patchregion (Figures 7 & 8 on the right), tensile stresses show up in the patch that are predicted

only by including the sequential loading.

Figure 9 illustrates in more detail the vertical stress histories based on the incremental

path dependent loading. The pairs of points in the area of the patch illustrate the local

bending stresses induced after the repair and subsequent re-tensioning of the tendons.This effect is not accurately predicted without a path dependent solution.


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FIGURE 9VERTICAL STRESS HISTORIES @HOLE ELEVATION

The differences between the inside and outside surface stresses in the containment wall

around the patch are increased by the separation of the patch and the wall that occurs

when the grout bond is ineffective. A breaking stiffness can be defined analytically tocapture this response using advanced contact element settings. If the repair and

subsequent grout are ineffective in developing any tensile bond to the existing concrete, astandard contact formulation is used in the model. Contact elements will simulate only a

compressive load transfer after the bond is broken in both methods. Figure 10 illustrates

the contact status around the edge of the opening after repair and re-tensioninging for the

example building. Separation is predicted locally on the top and bottom inside surfaces ofthe patch-wall interface. By including this effect, any potential tensile load transfer is

redistributed to the surrounding elements.

FIGURE 10CONTACT STATUS OF PATCH -WALL INTERFACE

Specific example demonstrating the re-distribution of loading

A further demonstration on the effects of the hole and subsequent patch can bedemonstrated with a simple analysis. Figure 11 illustrates the simple finite element

model used in this demonstration.


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FIGURE 11-STEP1 --WALL UNDER AXIAL LOADING CONDITIONS

Four analysis steps are performed with the simple model to illustrate the effects of the

patch load re-distribution on a smaller scale model. The simplified model includes a flatwall with a patch region. Symmetry boundary conditions are imposed on the sidewalls,

the base is fixed and a vertical displacement is applied to the top of the wall. The four

stage loading event is performed as follows:

1. Load the wall under uniform axial displacement (The axial compression replicates

the effect of the tendon loads) - Measure the stress state in the pre- repaired wall.

2. Reduce the displacement and create a hole in the wall simulating the creation ofthe construction opening.

3. Patch the hole under the same reduced displacement (Use element birth)

4. Increase the loads (uniform axial displacement) back to its original values (This

replicates the re-tensioning of the tendons) and compare with original wall

The table below illustrates the increase in stress that occurs at the edge of the patch when

the tendons are re-tensioned. This effect is the redistributed load path where the patchregion cannot return to its original stress state and thus the surrounding wall must

compensate by carrying more load. This will be the stress state after repair. Future items

to consider will be that during aging and subsequent relaxation of the tendons, thebuilding wants to redistribute its loads, thus the patch will pickup more stresses

eventually, which will in-turn, relieve the area around the patch.

Load Step Number Max. Vertical Stress Minimum Vert. Stress

1 Uniform Load 1648 1648

2 Hole in Wall 435 0

3 Hole Patched 435 0

4 Loads Increased 1754 1319


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The following stress plots further illustrate this stress redistribution effect. Notice that

when the loads are re-applied to the wall after patching, the stress distribution stillfollows the post-patched shape, although the magnitudes of stress increase everywhere.

FIGURE 12STEP 1AXIAL STRESS RESULTSUNIFORM STRESS STATE IN WALL

FIGURE 13:STEP 2&3AXIAL STRESSHOLE CREATED/REPLACED IN THE WALL UNDER REDUCED LOADS


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FIGURE 14:STEP4AXIAL STRESS RESULTSHOLE REPLACED IN THE WALL WITH ORIGINAL LOADS

NOTICE THE STRESS IN THE HOLE IS SMALLER THAN THE ORIGINAL CONDITION AND INCREASED AT THE EDGE

OF THE HOLE.

MODELING VALIDATION

Validation of the modeling techniques described in this paper can be derived from the

ANSYS documentation [1]. All of the techniques incorporated in ANSYS have been

validated against closed form solutions or test data. A subset of ANSYS validationproblems relevant to the analytical models described in this paper include:

VM194 - Element Birth/Death in a Fixed BarVM31 - Cable Supporting Hanging Loads (Initial Strain Example)

VM146 - Bending of a Reinforced Concrete Beam (Concrete Example)

VM211 - Rubber Cylinder Pressed Between Two Plates (Contact Example)

CONCLUSIONS

This paper demonstrates that using nonlinear incremental finite element based stress

analysis to simulate the repair of post-tensioned concrete containment buildings predicts

stresses that would not be captured using either shell modeling or non-path dependent

simulations. Key modeling techniques include:

Explicit modeling of the tendons and abutments to accurately capture force,

displacement and stress results.

Step-by-step loading where intermediate results are captured.


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Element Birth and Death modeling that captures the true response of creating andrepairing construction openings.

Automated analysis files with user-friendly input parameters such that allow the

designer to perform design iterations without becoming an analysis expert.

REFERENCES

[1] ANSYS, Inc., "ANSYS Verification Manual", Release 10.0 Documentation for ANSYS, July 18,2005.

structural analysis of post-tensioned concrete containment building repair using 3-d finite elements

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