ML19205A496

NER027 - Saouma, V., Benchmark Problems for Aar Fea Code Validation (Aug. 4, 2017)

ML19205A496
Person / Time
Site:	Seabrook
Issue date:	07/24/2019
From:	Morgan, Morgan, Lewis & Bockius, LLP, NextEra Energy Seabrook
To:	Atomic Safety and Licensing Board Panel
SECY RAS
References
50-443-LA-2, ASLBP 17-953-02-LA-BD01, RAS 55113
Download: ML19205A496 (37)

Text

UNITED STATES OF AMERICA NUCLEAR REGULATORY COMMISSION ATOMIC SAFETY AND LICENSING BOARD In the Matter of Docket No. 50-443-LA-2 NEXTERA ENERGY SEABROOK, LLC ASLBP No. 17-953-02-LA-BD01 (Seabrook Station, Unit 1)

Hearing Exhibit Exhibit Number: NER027 Exhibit

Title:

Saouma, V., Benchmark Problems for AAR FEA Code Validation (Aug. 4, 2017)

RILEM Technical Committee 259-ISR Benchmark Problems for AAR FEA Code Validation Victor Saouma1 Alain Sellier2 Stephane Multon2 Yann Le Pape3 M-Amin Hariri-Ardebili1 af t 1

University of Colorado, Boulder, USA 2

Dr Universite de Toulouse, France 3

Oak Ridge National Laboratory, USA August 4, 2017 For latest versions.

Contents 1 Introduction 1 1.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Important Factors in Reactive Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Test Problems 5 2.1 P0: Finite Element Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.1 P1: Constitutive Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.1.1 Constitutive Model Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.1.2 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.2 P2: Drying and Shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.2.1 Constitutive Model Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.2.2 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.3 P3: Basic Creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.3.1 Constitutive Model Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.3.2 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.4 P4: AAR Expansion; Temperature Eect . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.4.1 Constitutive Model Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.4.2 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.5 P5: Free AAR Expansion; Eect of RH . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.5.1 Constitutive Model Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.5.2 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.6 P6: AAR Expansion; Eect of Con"nement . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.6.1 Constitutive Model Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.6.2 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3 Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3.1 P7: Eect of Internal Reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3.1.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3.1.2 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3.2 P8: Reinforced Concrete Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3.2.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3.2.2 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 i

ii CONTENTS 2.3.3 P9: AAR Expansion; Idealized Dam . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3.3.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3.3.2 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3.4 P10: Expansion of RC Panel With or Without Lateral Con"nement . . . . . . . . . . 19 2.3.4.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.3.4.2 Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.3.5 P11: AAR Expansion of Nuclear Containment Vessel Followed by Earthquake . . . . . 26 2.3.5.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.3.5.2 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.3.5.2.1 Static . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.3.5.2.2 Dynamic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3 Results Submission and Workshop 29 3.1 Excel "le for Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2 Workshop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

List of Figures 2.1 Deterioration of AAR aected concrete (Capra and Sellier, 2003) . . . . . . . . . . . . . . . . 6 2.2 Drying and Shrinkage test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Mass variations for non reactive concrete under various RH conditions; (multon03) . . . . . 7 2.4 Strain variations for non reactive concrete under various RH conditions; (multon03) . . . . . 8 2.5 Humidity variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.6 Creep in non-reactive concrete under sealed condition for dierent axial stress; (multon03) . 9 2.7 Stress variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.8 Free expansion from Larives tests;(Larive:1998) . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.9 Temperature variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.10 Mass variation for reactive concrete under various RH conditions; (multon03) . . . . . . . . 11 2.11 Strain variation for reactive concrete under various RH conditions;(multon03) . . . . . . . . 11 2.12 No vertical stress, no con"nement (free swelling);(multon03) . . . . . . . . . . . . . . . . . . 12 2.13 10 MPa vertical stress, no con"nement; (multon03) . . . . . . . . . . . . . . . . . . . . . . . 13 2.14 Vertical stress of 10 MPa and concrete cast in a 5 mm thick steel container; (multon03) . . 13 2.15 Vertical stress of 10 MPa and concrete cast in a 5 mm steel container; (multon03) . . . . . . 13 2.16 Concrete prism with internal reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.17 Multons Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.18 Mass variation of the beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.19 Idealized dam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.20 Yearly variation of pool elevation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.21 Specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.22 Stress Strain curve (28 days) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.23 Concrete expansion block tested by Prof. E. Giannini . . . . . . . . . . . . . . . . . . . . . . 23 2.24 Laboratory measured expansion. Error bars: standard deviation. . . . . . . . . . . . . . . . . 24 2.25 Location of internal concrete gauges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.26 Location of deformation sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.27 Characteristics of the NCVS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.1 Sample of Excel based presentation of results . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 iii

List of Tables 1.1 List of Benchmark Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1 Characteristics of the three specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 Target mix design . Aggregate quantities are for oven-dry material. Water quantities assume aggregates in saturated-surface dry (SSD) condition. () To limit the early-age temperature below 65o C, about 70% of the water was added to the mix as ice cubes. . . . . . . . . . . . 21 2.3 Reported 28 days compressive strengths fc (MPa) . . . . . . . . . . . . . . . . . . . . . . . . 21 2.4 Reported 28 days tensile strengths ft (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.5 Reported 28 days elastic modulus Ec (GPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.6 Provided shrinkage curve data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.7 Provided expansion curve data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.8 Strain gauges location points. S refers to KM embedded sensors, while R refers to resistive strain gauges placed directly on the rebars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.9 Deformation sensor location points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 iv

1 Introduction A number of structures worldwide are known to (or will) suer from chemically induced expansion of the concrete. This includes not only the traditional alkali aggregate reaction (also known as alkali silica reaction) but increasingly delayed ettringite formation (DEF)1 .

There are three components to the investigation of structures suering from such an internal deterioration:

a) Chemo-physical characterization focusing primarily on the material; b) Computational modeling of the evolution of damage and assessing the structural response of the structure; and c) managing the structure, (Divet et al., 2003).

Focusing on the second one, ultimately an engineer must make prediction for the response of a structure.

In particular: a) is the structure operational, b) is it safe, and c) how those two criteria will evolve in time.

This task is best addressed through a numerical simulation (typically "nite element analysis) which should account for most of the structures inherent complexities. This is precisely the object of this document.

The assessment of these "nite element codes has been partially assessed within the ICOLD International Benchmark Workshops on Numerical Analysis of Dams2 , and there were only limited discussion of AAR within the European project Integrity Assessment of Large Concrete Dams, NW-IALAD, however there has not yet been any rigorous and rational assessment of codes. Similar recent benchmark analyses of shear walls subjected to reverse cyclic load following AAR expansion, highlighted the need for a more comprehensive benchmark.

Ultimately, practitioners would like to be able to calibrate their model with the limited historical "eld observation (typically inelastic crest displacements for dams, or crack maps for reinforced concrete) and then use it to extrapolate the behavior of the existing or modi"ed structure into the future. In science and engineering, any extrapolation should be based on a fundamentally sound model which ideally should be independently assessed for its capabilities. Unfortunately, expansive concrete ("nite element) models have not yet been assessed within a formal framework. The objective of this eort is indeed an attempt to develop such a formal approach for the bene"t of the profession.

Though we are aware of the importance of the chemical constituents of a reactive concrete (part a above),

and their potential impact on the residual swelling, this aspect is not considered in this study. Henceforth, we limit ourselves to the interaction of various mechanical aspects: temperature, relative humidity, chemically induced swelling, and mechanical load.

The authors believe that prior to the comparison of analysis of a structures, a series of simple tests should "rst be undertaken. Each one of the test problems in turn will highlight a strength (or de"ciency) of 1 It is well known that DEF is often associated with AAR, however it is increasingly observed that it can occur by itself in massive concrete structure subjected to early age high temperature and under high relative humidity (above 95%).

2 The sixth (Salzburg) and the eighth (Wuhan) benchmarks invited participants to analyze Pian Telessio and Poglia dams respectively. There was no submission to the former, and only two for the second.

1

2 1.1. OBJECTIVES a model, one at a time. Then and only then, we could assess a model predictive capabilities for the analysis of a structure.

This document will describe such a series of tests, and format in which data should be reported. In order to facilitate comparison, the test problems are of increasing complexity. For the most part we assess one parameter at a time, then two, and then three. Only after such an exercise could we compare full blown dam and nuclear containment vessel structure subjected to static and dynamic load.

1.1 Objectives This document is submitted by the authors to the Engineering community for the assessment of "nite element codes which can perform a modern simulation of reactive concrete expansion.

The study is composed of two parts, the "rst addresses material modeling, and the second structure modeling. For the material modeling each study is split in two parts: a) parameter identi"cation for the constitutive model (through calibration of your model with provided laboratory test results); and b) Predic-tion.

1.2 Important Factors in Reactive Concrete Assuming that the "nal residual swelling of the reactive concrete is known, and based on experimental and "eld observations, indications are that the following factors3 should be considered in the "nite element analysis of a structure:

1. Environmental Conditions of the concrete (a) Temperature (b) Humidity

2. Constitutive models (a) Solid concrete (tension, compression, creep, shrinkage)

(b) Cracks/joints/interfaces.

3. Load history

4. Mechanical Boundary Conditions (a) Structural Arrangement (b) Reinforcement (c) Anchorage 1.3 Problems Table 1.1 describes the 11 problems de"ned. It should be understood that not all participants will contribute to all of them, but to most of them.

3 There is no general agreement on the importance of all these parameters, the list is intended to be inclusive of all those perceived by researchers to be worth examining.

RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

CHAPTER 1. INTRODUCTION 3 No. Description P0 Textual description of "nite element code/models Material Response P1 Constitutive model P2 Capturing drying and shrinkage P3 Capturing creep P4 Eect of Temperature P5 Eect of RH P6 Eect of con"nement Structural Response P7 Internal reinforcement P8 Reinforced concrete beam P9 Dam (simpli"ed)

P10 Reinforced concrete panel expansion P11 Nuclear containment vessel (Simpli"ed)

Table 1.1: List of Benchmark Problems RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

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2 Test Problems 2.1 P0: Finite Element Model Description Provide up to "ve pages of description of the model adopted in this particular order:

Constitutive Model

1. Basic principles of the model and its implementation.

2. Nonlinear constitutive model of sound or damaged concrete (clarify)

(a) Instantaneous response (elasticity, damage, plasticity, fracture and others)

(b) Delayed response (creep and shrinkage)

3. Eect on the chemically induced expansion by (a) Moisture (b) Temperature (c) Stress con"nement

4. Eect on the mechanical properties of concrete by (a) Expansion (b) Shrinkage and creep Finite Element Code Features

1. Gap Element

2. Coupled hydro-thermo-mechanical

3. Others 2.2 Materials In light of the preceding list of factors in"uencing AAR, the following test problems are proposed. All results are to be entered in the accompanying spreadsheet and formatting instruction strictly complied with (to facilitate model comparison).

2.2.1 P1: Constitutive Models At the heart of each code is the constitutive model of concrete. This problem will assess the code capabilities to capture the nonlinear response in both tension and compression.

It should be noted that in some codes, (Sellier et al., 2009) the constitutive model is tightly coupled (in parallel) with the AAR expansion one (modeled as an internal pressure), in other, (Saouma and Perotti, 2006) 5

6 2.2. MATERIALS it is more loosely coupled (in series) with the AAR (modeled as an additional strain).

2.2.1.1 Constitutive Model Calibration Perform a "nite element analysis of a 16 by 32 cm concrete cylinder with fc , ft and E equal to 38.4 MPa, 3.5 MPa and 37.3 GPa respectively1 . Traction is applied on the top surface, and a frictionless base is assumed.

Make and state any appropriate assumption necessary, use the following imposed strain histogram:

ft f

0 1.5 0 3 t 1.5c 0 3c (2.1)

E E where c = 0.002. If needed, the fracture energy GF in tension and compression are equal to 100Nm/m2 and 10,000 Nm/m2 respectively.

2.2.1.2 Prediction Units: m, sec., MN, and MPa.

Repeat the previous analysis following an AAR induced expansion of 0.5%, you may use the experimen-tally obtained degradation curve, by (Institution of Structural Engineers, 1992) and published by Capra and Sellier ( (2003)), Fig. 2.1 Normalized Compression (ISE 92) Normalized Tension (ISE 92)

Normalized Young Modulus (ISE 92) Normalized Young Modulus (Larive 97) 1.20 1.00 Normalized Value 0.80 0.60 0.40 0.20 0.00 0 0.2 0.4 0.6 0.8 1 Swelling [%]

Figure 2.1: Deterioration of AAR aected concrete (Capra and Sellier, 2003)

Results to be tabulated in the accompanying spreadsheet.

2.2.2 P2: Drying and Shrinkage For some structures not necessarily under water (such as bridges or certain hydraulic structures), drying shrinkage strains may be of similar order of magnitude as the AAR induced ones. As shown in Fig. 2.2 one must consider various cases of drying and shrinkage, reactive and non reactive concrete, and at relative humidities ranging from a low 30% to a fully saturated environment, and sealed or not. There are a total of 6 potential cases of interest:

a. Non reactive concrete at 30% RH

b. Reactive concrete at 30% humidity 1 These parameters should be used in all subsequent test problems.

RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

CHAPTER 2. TEST PROBLEMS 7

c. Non Reactive concrete sealed specimen

d. Non Reactive concrete under water.

e. Reactive Concrete, sealed cylinder.

f. Reactive concrete under water.

which will be analyzed in P2 and P5 free f) R 100% H e) R Sealed d) NR 100%

H c) NR Sealed Time b) R 30% H a) NR 30% H Figure 2.2: Drying and Shrinkage test Cases 2.2.2.1 Constitutive Model Calibration Fit your parameters using a 16 by 32 cm cylinder by performing the following analyses: a, c, and d with respect to the temporal variation of mass (Fig. 2.3) and longitudinal strain (Fig. 2.4)

Mass, Fig. 2.3 and strain, Fig. 2.4 temproal variation2 .

2.0 Sealed Water 30% RH 1.0 Mass variation (%)

0.0

-1.0

-2.0

-3.0

-4.0 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 Time (day)

Figure 2.3: Mass variations for non reactive concrete under various RH conditions; (multon03) 2 All available experimental results are tabulated in separate Excel "les.

RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

8 2.2. MATERIALS 0.03 water Sealed 30% RH 0.02 0.01

% Strain 0.00

-0.01

-0.02

-0.03

-0.04

-0.05 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 Time (day)

Figure 2.4: Strain variations for non reactive concrete under various RH conditions; (multon03) 2.2.2.2 Prediction Units: m, sec., MN, and MPa.

Using the parameter determined from the previous section, repeat the same analysis with the temporal variation of external RH for the cylinder shown in Fig. 2.5.

 

RHmax RHmin t 16 RHmax RHmin RH(week) = sin 2 + (2.2) 2 52 2 where RHmax and RHmin are equal to 95% and 60% respectively.

Yearly External Humidity Variation 100.0 80.0 RH [%]

60.0 40.0 0 10 20 30 40 50 Time [Weeks]

Figure 2.5: Humidity variation Results to be tabulated in the accompanying spreadsheet.

2.2.3 P3: Basic Creep There is strong experimental and "eld indications that creep plays a dominant role in the irreversible long term deformation concrete subjected to constant load. Its eect must be accounted for to properly extract the AAR expansion. This may be explained through biaxially or triaxially loaded elements where swelling is restricted in one direction while free to occur on the other(s). Therefore, in the AAR constrained direction creep deformation will be predominant. This is more likely to occur in arch dams.

RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

CHAPTER 2. TEST PROBLEMS 9 2.2.3.1 Constitutive Model Calibration For a 13 by 24 cm cylinder subjected to 10 and 20 MPa axial compression, plot the longitudinal and radial displacements. You may calibrate your model on the experimental curve shown in Fig. 2.6.

Creep of Non Reactive Concrete with 10 and 20 MPa Axial Stress 0.05 0.00

-0.05 Strain (%)

-0.10

-0.15 Axial 10MPa Radial 10MPa

-0.20 Axial 20MPa Radial 20MPa

-0.25

-0.30 0 50 100 150 200 250 300 350 400 450 Time (day)

Figure 2.6: Creep in non-reactive concrete under sealed condition for dierent axial stress; (multon03) 2.2.3.2 Prediction Units: m, sec., MN, and MPa.

Using the previously determined parameters, repeat the same analysis for the axial load history shown in Fig. 2.7.

Yearly Axial Traction Variation

-5 Stress [MPa]

-6

-7

-8

-9

-10 0 10 20 30 40 50 Time [Weeks]

Figure 2.7: Stress variation Results to be tabulated in the accompanying spreadsheet.

2.2.4 P4: AAR Expansion; Temperature Eect All chemical reactions are thermodynamically driven. Reactive concrete expansion varies widely with tem-perature ranges usually encountered in the "eld or laboratories. Hence, it is of paramount importance that the kinetics of the reaction captures this dependency.

RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

10 2.2. MATERIALS 2.2.4.1 Constitutive Model Calibration Perform the "nite element analysis of a 13 by 24 cm cylinder under water, free to deform at the base and undergoing a free expansion, and for T = 23o C and 38o C. Fit the appropriate parameters of your model with Fig. 2.8 obtained by Larive:1998 Bétons réactifs, cylindres 1324 , en enceinte humide Gonflt longitudinal (jours) 0.25 0.20 0.15 0.10 Incertitude élargie sur la mesure 0.05 Conservation 38°C Conservation 23°C 0.00 0 100 200 300 400 500 600 Temps( jours)

Figure 2.8: Free expansion from Larives tests;(Larive:1998) 2.2.4.2 Prediction Units: m, sec., MN, and MPa.

Repeat the previous analysis using the variable internal temperature

 

Tmax Tmin t 16 Tmax Tmin T (week) = sin 2 + (2.3) 2 52 2 where Tmax and Tmin are equal to 25o C and 0o C respectively, as shown in Fig. 2.9 Yearly External Temperature Variation 30.0 25.0 Temperature [oC]

20.0 15.0 10.0 5.0 0.0 0 10 20 30 40 50 Time [Weeks]

Figure 2.9: Temperature variation Results to be tabulated in the accompanying spreadsheet.

RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

CHAPTER 2. TEST PROBLEMS 11 2.2.5 P5: Free AAR Expansion; Eect of RH Relative humidity plays a critical role in the expansion of AAR aected concrete. It is well established, (Poole, 1992) that expansion will start for a RH at least equal to 80%, and will then increase with RH (RH 8 is a widely accepted forumula). For external bridge structures and some dams this can be critical.

2.2.5.1 Constitutive Model Calibration Using a 16 by 32 cm cylinder, and assuming a temperature of 38oC, "t the appropriate parameters for mass and vertical strain variation of reactive concrete as shown in Fig. 2.10 and 2.11 respectively.

Water Sealed 30% RH 2.0 1.0 Mass variation (%)

0.0

-1.0

-2.0

-3.0

-4.0

-5.0 0 50 100 150 200 250 300 350 400 450 500 Time (day)

Figure 2.10: Mass variation for reactive concrete under various RH conditions; (multon03)

Water Sealed 30% RH 0.30 0.20

% Strain 0.10 0.00

-0.10 0 50 100 150 200 250 300 350 400 450 500 Time (day)

Figure 2.11: Strain variation for reactive concrete under various RH conditions;(multon03) 2.2.5.2 Prediction Units: m, sec., MN, and MPa.

Repeat previous analysis using the RH variation shown in Fig. 2.5.

RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

12 2.2. MATERIALS Results to be tabulated in the accompanying spreadsheet.

2.2.6 P6: AAR Expansion; Eect of Con"nement It has long been recognized that con"nement inhibits reactive concrete expansion, (Charlwood et al., 1992),

(Leger, Cote, and Tinawi, 1996) and most recently (Multon and Toutlemonde, 2006). This test series seeks to ensure that this is properly captured by the numerical model.

2.2.6.1 Constitutive Model Calibration For a 13 by 24 cm cylinder, and assuming a temperature of 38oC, analyze the following test cases (all of which consist of sealed specimens):

P6-a. No vertical stress, no con"nement (Free swelling), Fig. 2.12.

Axial Radial 0.100 0.080 0.060

% Strain 0.040 0.020 0.000

-0.020 0 50 100 150 200 250 300 350 400 450 500 Time (day)

Figure 2.12: No vertical stress, no con"nement (free swelling);(multon03)

P6-b. Vertical stress of 10 MPa, no con"nement, Fig. 2.13.

P6-c. No vertical stress, concrete cast in a 5 mm thick steel container, Fig. 2.14.

P6-d. Vertical stress of 10 MPa and concrete cast in a 5 mm thick steel container, Fig. 2.15.

In all cases, plot both the axial and radial strains.

2.2.6.2 Prediction Units: m, sec., MN, and MPa.

Repeat the analysis with the vertical and radial imposed stress histogram shown in Fig. 2.7.

Results to be tabulated in the accompanying spreadsheet.

RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

CHAPTER 2. TEST PROBLEMS 13 Axiall Radiall 0.100 0.075 0.050 0.025 0.000

% Strain

-0.025

-0.050

-0.075

-0.100

-0.125

-0.150 0 50 100 150 200 250 300 350 400 450 500 Time (day)

Figure 2.13: 10 MPa vertical stress, no con"nement; (multon03)

Free Expansion with 5mm confinement 0.18 0.16 Axial Radial 0.14 0.12 Strain (%)

0.10 0.08 0.06 0.04 0.02 0.00

-0.02 0 50 100 150 200 250 300 350 400 450 Time (day)

Figure 2.14: Vertical stress of 10 MPa and concrete cast in a 5 mm thick steel container; (multon03) 10 MPa Axial Stress and 5mm confinement 0.06 0.04 0.02 Strain (%)

0.00

-0.02

-0.04 Axial Radiall

-0.06

-0.08

-0.10 0 50 100 150 200 250 300 350 400 450 Time (day)

Figure 2.15: Vertical stress of 10 MPa and concrete cast in a 5 mm steel container; (multon03)

RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

14 2.3. STRUCTURES 2.3 Structures 2.3.1 P7: Eect of Internal Reinforcement 2.3.1.1 Description Internal reinforcement inhibits expansion and AAR induced cracking would then align themselves with the direction of reinforcement as opposed to the traditional map cracking. This test problem seeks to determine how the numerical model accounts for this, especially when cracking (thus a nonlinear analysis is needed) occurs.

Analyze the cylinder of P6-a under the same condition (free expansion, 38oC, 100% RH), for the same duration with a single internal reinforcing bar of diameter 12 mm in the center, and E=200,000 MPa and fy =500 MPa.

2.3.1.2 Prediction Units: m, sec., MN, and MPa.

Determine longitudinal strain in the rebar and the longitudinal and radial strains on the surface of the concrete cylinder. In both cases values are to be determined at mid-height.

rebar 240 mm 130 mm Figure 2.16: Concrete prism with internal reinforcement Results to be tabulated in the accompanying spreadsheet.

2.3.2 P8: Reinforced Concrete Beams 2.3.2.1 Description The mechanical behavior of two concrete beams, studied by S. Multon during his Ph.D. works at LCPC, is proposed. One beam is damaged by ASR during two years exposure in a 38o C environment and dierential water supply, leading to dierential ASR expansion within the structures. The other made with non-reactive aggregates was stored in similar conditions. Namely, the eects of the ASR development have been quanti"ed in a 4-points bending test of the beams, resulting in a lot of data among which the residual stiness and the "exural strength of both reactive and non-reactive beams. The objective is to simulate the evolution of the two beams during the two years of tests, and to "nish by a simulation of beam failure in four points bending.

RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

CHAPTER 2. TEST PROBLEMS 15 250 mm 3m 2.8m during drying - watering cycles Figure 2.17: Multons Beams Material characteristic are the same then in tests P1 to P6, therefore, the LCPC performed tests at several dates since the fabrication (all the results are given in Table 1) insert table The whole experimental plan of LCPC involves several beams as mentioned in table 2. In the present benchmark only beams P4 and P6 have to be simulated.

RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

16 2.3. STRUCTURES As AAR depends on humidity, a humidity pro"le must be "tted, in order to consider eect of saturation on the reaction. In order to "t the drying-humidi"cation cycle, the mass evolutions of the beams are given bellow Figure 2.18: Mass variation of the beams The temperature is constant and equal to 38o C. The concrete porosity is around 16% (15% at the bottom and 17% at the top of the beam).

2.3.2.2 Prediction Units: m, sec., MN, and MPa.

• The "rst objective is to "nd a realistic humidity pro"le compatible with the mass variation history given in "gure 2.17.

• The second objective is to predict the de"ection of each beam, at mid span, versus time

• The third objective is the evolution of stress versus time, in the bottom longitudinal reinforcement

1. 16, at mid span.

• The last stage consists to simulate, for the two beams, a four point bending test schematized in Fig.

2.18. Participants have to provide the Force-de"ection curve until failure of each beam.

Results to be tabulated in the accompanying spreadsheet.

2.3.3 P9: AAR Expansion; Idealized Dam 2.3.3.1 Description This last test problem assesses the various coupling amongst various parameters as well as the "nite element code and its ability to simulate closure of joint. A common remedy for AAR induced damage in dams is to cut a slot in the structure as in Mactaquac (Gilks and Curtis, 2003). This will relieve the state of stress, and allow the concrete to expand freely. However, at some point concrete swelling will result in a contact between the two sides of the slot. Hence, this problem will test the model ability to capture this important simulation aspect as well.

Consider the reduced dam model shown in Fig. 2.19 with the following conditions: a) lateral and bottom faces are all fully restrained; b) front back and top faces are free; c) slot cut at time zero, total thickness 10 RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

CHAPTER 2. TEST PROBLEMS 17 cm; d) concrete on the right is reactive, and concrete block on the left is not reactive; e) hydrostatic pressure is applied only on the right block.

z m

10 A

80 m h 10 mm R

y 50 20 m m

x 15 m 15 m Figure 2.19: Idealized dam 2.3.3.2 Prediction Units: m, sec., MN, and MPa.

Using the "tting data of P6, and an friction angle of 50o C for concrete against concrete, and zero cohesion, consider two cases:

• Homogeneous "eld of internal temperature (20 C), relative humidity (100%), and an empty reservoir.

• Transient "eld of external temperature Fig. 2.9, relative external humidity Fig. 2.5, and pool elevation variation Fig. 2.20 given by where ELmax and ELmin are equal to 95 and 60 respectively.

For both analysis, the speci"ed temperature and relative humidity is the one of the concrete surface.

Zero "ux condition between dam and foundation. Reference base temperature of the dam is 20o C.

• x, y, z displacements of point A.

• Fx, Fy and Fz resultant forces on the "xed lateral face versus time (25 years). Assume the typical yearly variations of external air temperature and pool elevation shown in Fig. 2.9 and 2.20 respectively.

This model seeks to capture: a) general "nite element program capabilities in modeling the joint response; b) ease (or diculty in preparing the input data "le for a realistic problem; and c) coupling of the various parameters.  

ELmax ELmin t ELmax ELmin EL(week) = sin 2 + (2.4) 2 52 2 where ELmax and ELmin are equal to 95 and 60 respectively.

RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

18 2.3. STRUCTURES Yearly Variation of the Pool Elevation 100.0 95.0 90.0 Elevation [m]

85.0 80.0 75.0 70.0 65.0 60.0 0 10 20 30 40 50 Time [Weeks]

Figure 2.20: Yearly variation of pool elevation Results to be tabulated in the accompanying spreadsheet.

RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

CHAPTER 2. TEST PROBLEMS 19 2.3.4 P10: Expansion of RC Panel With or Without Lateral Con"nement This section has been prepared with the assistance of Nolan Hayes, Ammar Abd-Elssamd and Qiang Gui from the University of Tennessee, Knoxville.

The University of Tennessee, Knoxville (UTK), under U.S. Department of Energy (DOE) subcontract managed by Oak Ridge National Laboratory (ORNL), have been performing large scale laboratory testing of con"ned and uncon"ned concrete blocks (simulating a typical reinforced concrete member found in light water reactor nuclear power plants).

The objective of this benchmark test case is to perform predictive numerical simulations of two large-scale reinforce concrete blocks (with dierent boundary conditions) and compare the simulation results with the already collected monitoring data.

2.3.4.1 Description Geometry The laterally-con"ned reinforced concrete reactive specimen, referred to as CASR (C for con-

"ned), is cast inside a rigid steel frame while a similar reinforced concrete reactive specimen, referred to as UASR (U, for uncon"ned) is allowed to expand without lateral restraints. A third specimen, non-reactive, referred to as CTRL, for control, is also not subjected to lateral restraints. See summary in Table 2.1 All three specimens of dimensions, 136 x 116 x 40 (length, width and height; x-y-z axis), i.e., 3.453 m x 2.946 x 1.016 m, Fig. 2.21 are reinforced near the top and the bottom faces by two welded layers of orthogonal rebars: (22) #11 bars (1.41 nominal diameter, cross section area: 1006 mm2 ), (10) in one direction and (12) in the perpendicular direction, placed in horizontal planes - See Fig. 2.21(d) for layout. Rebars are made of standard carbon steel. Square plate heads (4 x 4 x 1, i.e., 10.16 cm x 10.16 cm x 2.54 cm) are welded to the rebar extremities. The concrete cover, in the least distance to the concrete outer surface, is 3 (7.62 cm). There is no reinforcement in the third, i.e.,

vertical, direction, to the exception of (6) #11 debonded rebar spacers placed inside of pipes to allow free vertical expansion during the test.

Steel Con"nement Frame The steel plate girder frame was designed with the primary goal of maximizing stiness in bending. In order to achieve this goal, 3 thick plates, height 34, were chosen as "anges to the plate girder. These "anges are connected by three 2 thick web plates, length 210. All steel was manufactured from A572 Grade 50 steel plate. Design of splice plate connection not provided here is available upon request.

In order to reduce frictional eects between the steel frame and the concrete specimen, a single layer (thickness: 1.5 mm) of high-density polyethylene (HDPE) was introduced at the interface, provid-ing a low steel-HDPE friction coecient estimated by the vendor around 0.3 and unilateral contact conditions.

Additional Post-tensioned system Four threadbar post-tension bars (2 in each direction, 2.5 inches dia.)

Table 2.1: Characteristics of the three specimens ID Label Con"ned Reactive 1 CASR Yes Yes 2 UASR No Yes 3 CTRL No No RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

20 2.3. STRUCTURES (a) Computer rendering of the con"ned specimen (CASR) (b) Form construction in UTK Civ. Env. Eng. high bay 11'-4" = 136" 1'-1" 10" 10" 5" 5" 10" 10" 10" 10" 10" 10" 10" 10" 1'-1" x

1'-1" 10"

• 1 1 1

10" 10" 1

5" 1 5" 1 1 1 3 9'-8" = 116" 10" 10" 1

10" 10" 10" 1'-1" y

(c) Con"ned specimen layout - Top view. (Shaded area in- (d) Reinforcement layout - Top view. Bottom and top rein-dicating symmetries) forcement layout are identical.

Figure 2.21: Specimens manufactured by DYWIDAG-Systems International (DSI) were installed in September 2016, in order to increase the con"ning force, if necessary. It is initially just slightly tightened to avoid slack, and has remained, as of today.

Casting and Curing Casting took place July 23rd 2016. In an attempt to mitigate potential crack sources other than ASR, the formworks were insulated by placing rigid foam sheathing insulation with an R-value of three around the side and on top of the specimens, shortly after pouring. The insulation was placed with edges overlapping and secured in place with tape and plastic wrap.

All formworks were removed on August 4, 2016. Each large specimen and concrete cylinder, for further materials testing, was covered with wet burlap to prevent moisture loss. The burlap was periodically moistened as required to keep the concrete surfaces wet.

A few days after casting, the bottom support is removed, and the concrete block is vertically supported RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

CHAPTER 2. TEST PROBLEMS 21 by four 18 x 18 (45.7 cm x 45.7 cm) corner plates. Plates are directly supporting the specimens on the concrete surface. The estimated steel-concrete friction coecient is 0.6.

Operation A modular environmental chamber was designed by Norlake Scienti"c with the initial primary goals for temperature and humidity control being 100o F +/- 2o F (38o C +/- 1o C) and 95% +/- 5%. The chamber was initialized for full operation early morning August 19, 2016.

The chamber is periodically shutdown for inspection on a average frequency of 2 days per month.

During shutdowns, the average temperature and RH are about 77o F (25o C) and 60% (transient of about 4 hours4.62963e-5 days <br />0.00111 hours <br />6.613757e-6 weeks <br />1.522e-6 months <br />). After the shutdown period, the chamber is restarted and and the temperature and humidity return to the original set points within 6 hours6.944444e-5 days <br />0.00167 hours <br />9.920635e-6 weeks <br />2.283e-6 months <br />.

Target mix design The mix design has been extensively investigated at the University of Alabama, and the one retained, including a reactive and a control mix, is shown in Table 2.2 with 1 (25 mm) maximum size aggregate (MSA) composed of Green schist - muscovite, chlorite, quartz, Na-feldspar, K-feldspar, calcite, and, cristobalite.

In this mix, only the coarse aggregate is reactive. A 50% sodium hydroxide solution (NaOH) is used to increase the alkali loading of the reactive mix to 5.25 kg.m3 , and a 30% lithium nitrate solution (LiNO3) is used at 150% of the manufacturers recommended dosage to mitigate ASR for the control mix.

Table 2.2: Target mix design . Aggregate quantities are for oven-dry material. Water quantities assume aggregates in saturated-surface dry (SSD) condition. () To limit the early-age temperature below 65o C, about 70% of the water was added to the mix as ice cubes.

Quantity, kg.m3 (lb.yd3 )

Materials Reactive Control Coarse Aggregate 1180 (1988.8) 1180 (1988.8)

Fine Aggregate 728 (1226.6) 728 (1226.6)

Cement 350 (590) 350 (590)

()

Water 175 (295) 175 (295) w/c 0.5 0.5 NaOH solution 9.8 (16.6) -

LiNO3 solution - 11.9 (20.03)

Mechanical properties 28 days mechanical properties compressive and tensile strengths, and the elas-tic modulus are shown in Table 2.3, 2.4 and 2.5, respectively along with their mean and standard deviations.

Table 2.3: Reported 28 days compressive strengths fc (MPa)

Specimen Type AVG STD CASR 22.2 2.07 UASR 20.7 1.17 CASR: Con"ned Reactive Specimen UASR: Uncon"ned Reactive Specimen A representative 28 days stress-strain curve is shown in Fig. 2.22.

Shrinkage Shrinkage has been measured in the CTRL specimen. The datapoints for the shrinkage curve are shown in Table 2.6.

info to be added.

Expansion curves obtained from earlier material testing Expansion curves were obtained by Pr. E.

RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

22 2.3. STRUCTURES Table 2.4: Reported 28 days tensile strengths ft (MPa)

Specimen Type AVG STD CASR 2.70 0.215 UASR 2.13 0.044 CASR: Con"ned Reactive Specimen UASR: Uncon"ned Reactive Specimen Table 2.5: Reported 28 days elastic modulus Ec (GPa)

Specimen Type AVG STD CASR 34.5 3.03 UASR 34.4 2.22 CASR: Con"ned Reactive Specimen UASR: Uncon"ned Reactive Specimen Representative 28 days Stress-Strain 3500 3000 2500 Stress (psi) 2000 1500 1000 500 0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 Strain (in/in) x 10-3 Figure 2.22: Stress Strain curve (28 days)

Table 2.6: Provided shrinkage curve data Measured Shrinkage Age (Days) Shrinkage 5 -0.0031%

10 -0.0104%

20 0.0162%

30 -0.0178%

40 -0.0185%

50 -0.0190%

60 -0.0194%

100 -0.0214%

200 -0.0245%

300 -0.0275%

Giannini, at the University of Alabama (UA), while testing dierent aggregates-forming concrete. The concrete blocks, 300 x 300 x 600 mm, are stored in UA climate chamber at 38o C and 95%RH, shown in Fig. 2.23, and their expansion was periodically monitored using DEMEC points.

Data are tabulated in Table 2.7 and shown in Fig. 2.24 where the vertical expansions were taken over RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

CHAPTER 2. TEST PROBLEMS 23 Figure 2.23: Concrete expansion block tested by Prof. E. Giannini a 150 mm gauge length, and longitudinal expansions (same direction as longitudinal) were taken over a 500 mm gauge length. It should be noted that the reported mean (or average) corresponds to the average of all the experimental values.

Table 2.7: Provided expansion curve data Calculated Expansions Age (Days) Average Exp. STD 6 0.000% 0.0000%

40 -0.004% 0.0045%

68 0.000% 0.0031%

87 0.012% 0.0081%

103 0.020% 0.0091%

117 0.028% 0.0103%

138 0.045% 0.0193%

152 0.057% 0.0250%

170 0.070% 0.0307%

190 0.088% 0.0382%

220 0.103% 0.0440%

304 0.146% 0.0634%

312 0.157% 0.0733%

350 0.165% 0.0729%

371 0.174% 0.0782%

459 0.192% 0.0885%

504 0.197% 0.0903%

Recorders/sensors location Recorder3 locations are shown as follows:

Embedded KM strain transducer (KM-100B) , referred as strain gauges, gauge length 100 mm, in Fig. 2.25 and Table 2.8.

3 In a "nite element analysis, point from which we determine computed values are commonly referred to as recorders RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

24 2.3. STRUCTURES Figure 2.24: Laboratory measured expansion. Error bars: standard deviation.

Figure 2.25: Location of internal concrete gauges Continued on next page RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

CHAPTER 2. TEST PROBLEMS 25 Coord. [inches] Coord. [meter]

id dof x y z x y z Table 2.8: Strain gauges location points. S refers to KM em-bedded sensors, while R refers to resistive strain gauges placed directly on the rebars.

Coord. [inches] Coord. [meter]

ID DOF x y z x y z S1 1 58 53 25 1.473 1.346 0.635 S2 2 63 48 25 1.600 1.219 0.635 S3 3 53 43 10 1.346 1.092 0.254 S4 3 53 43 20 1.346 1.092 0.508 S5 3 53 43 30 1.346 1.092 0.762 R1 1 63 53 36.375 1.600 1.346 0.924 R2 2 63 53 34.875 1.600 1.346 0.886 Resistive strain gauges General purpose resistive strain gauges (gauge length: 1.52 mm) were at-tached to the reinforcing bars in the specimens. These sensors are attached to the top and bottom of the rebar in the select locations to measure rebar strain. The location of resistive strain gauges of interest are shown in Fig. 2.25 and Table 2.8.

Long gauges "ber-optics-based deformation sensors (SOFO, gauge length 1.0-1.5 m with location) measure (1) the vertical deformation between the bottom and top rebars layers, and, (2) horizontal deformation at the bottom surface as illustrated and tabulated in Fig. 2.26 and Table 2.9 Table 2.9: Deformation sensor location points Start Coord. [inches] End Coord. [inches] Start Coord. [meter] End Coord. [meter]

ID DOF x y z x y z x y z x y z D1 3 91 45 4.25 91 45 35.75 2.311 1.143 0.108 2.311 1.143 0.908 D2 3 45 71 4.25 45 71 35.75 2.311 1.143 0.108 2.311 1.143 0.908 D3 1 45 26 0 104 26 0 1.143 0.660 0 2.642 0.660 0 D4 1-2 38.75 28.75 0 89.75 79.75 0 0.984 0.730 0 2.280 2.026 0 Test duration Casting occurred July 23rd 2016. Assuming testing will end April 19, 2019, it is requested to model a total duration of 1,000-days.

2.3.4.2 Predictions Units: m, sec., MN, and MPa.

Plot for both specimens, CASR and UASR, as a function of time (increments of one month) the following RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

26 2.3. STRUCTURES Figure 2.26: Location of deformation sensors model outputs:

1. Vertical displacements at D1

2. Concrete strain at S1, S2, S3, S4 and S5.

3. Reinforcement strains at R1 and R2 Results to be tabulated in the accompanying spreadsheet.

2.3.5 P11: AAR Expansion of Nuclear Containment Vessel Followed by Earth-quake 2.3.5.1 Description Ultimately, codes should be able to analyze nuclear containment vessel structures suering from AAR under dynamic excitation.

Accordingly, a much simpli"ed geometry, inspired by NUREG/CR-6706 ( (2001)), is adopted. Fig.

2.27(a) shows the dimensions as well as the key material parameters. Note that the mat foundation and the walls only are subjected to AAR, the dome is not.

Total reinforcement is 1% vertically, and 0.5% circumferentially. Reinforcement in each direction is to be split in two layers, each 10 cm from the wall. Ignore reinforcement of the dome, however triple the elastic modulus of the concrete. Steel elastic modulus is 200 GPa, and yield stress 250 MPa.

RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

CHAPTER 2. TEST PROBLEMS 27 For added clarity, the boundary conditions, and the expansion curve is shown in Fig. 2.27(b). Only gravity and AAR loads are "rst considered. Note that the AAR expansion is assumed to follow Larives curve (Larive, 1998) 1 exp( tc )

(t) = (2.5) 1 + exp ( (tl) c )

C.L.

E = 40 Gpa 19 m = 0.2 0.76 m = 2,400 kg/m3 ft = 3.0 Mpa fc = 30 Mpa GF = 120 N/m A

1.4 m

= 0.5%

l = 10 years 37 m Z c = 5 years Y

X 3m (a) Geometery and Material Properties 1

0.5 AAR Volumetric Strain [%]

0.4 0.5 Intensity [g]

0.3 0

0.2 tlat tlat+2tcar -0.5 0.1 0 -1 0 5 10 15 20 25 30 35 40 0 5 10 15 20 Years Time [sec.]

(b) Expansion Curve (c) Expansion Curve Figure 2.27: Characteristics of the NCVS 2.3.5.2 Prediction Two sets of analyses are required:

RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

28 2.3. STRUCTURES 2.3.5.2.1 Static Though an axisymmetric analysis is possible, it is highly recommended that a 3D one (using 180 segment) be performed. Plot

1. Horizontal displacement of point A (x ) versus time (increments of one month).

2. Maximum (positive) principal stress ((1) ) in the wall versus time.

3. Crack pro"les at t = [5, 10, 20, 30] years 2.3.5.2.2 Dynamic Perform a 3D dynamic analysis, for a harmonic intensifying dynamic excitation, shown in Fig. 2.27(c),

assumed to occur at age t = 20 years. Assume a 5% Rayleigh damping. Report

1. Time of failure (may be de"ned when the analysis failed to converge).

2. Time displacement curves for point A starting with the AAR displacement that occurred at time 20 years, until failure (as de"ned by the user) occurs.

3. Maximum (positive) principal stress ((1) ) in the wall versus time.

4. Deformed shapes and crack pro"les at 1 sec. increment (starting with t = 0) until reported failure.

Results to be tabulated in the accompanying spreadsheet.

RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

3 Results Submission and Workshop 3.1 Excel "le for Results All results should be entered in the accompanying spreadsheet, Fig. 3.1. Note that the spreadsheet contains all available experimental data to facilitate "ts, and participants must enter their prediction within the prede"ned cells and for the speci"ed time increments. All cells are protected except those which can be overwritten by participant data.

This will greatly facilitate comparison of results, as a separate Matlab program could extract results from all submissions and results compared.

3.2 Workshop A RILEM workshop will be held in conjunction with the annual 2018 RILEM TC-259 committee to discuss results.

29

30 3.2. WORKSHOP (a) One tab for each Problem Names Affiliation email Country 1

2 3

Computer Programs 1

2 Comments (b) Identi"cation Test Case P10; Idealized Dam Model Fixed T, RH, Load Transient T, RH, Load Time Displacement (mm) Resultant Foce MN Displacement (mm) Resultant Foce MN Months x y z x y z x y z x y z 0

3 6

9 (c) Example of input cells Nuclear Containment Vessel Static AAR Dynamic (after AAR) years Ax [mm] (1) Mpa time [sec.] Ax [mm] (1) Mpa Failure at time:

0.00 0.00 0.50 0.01 1.00 0.02 1.50 0.03 2.00 0.04 InsertCrack profilet=5years InsertCrack profilet=1sec.

2.50 0.05 3.00 0.06 3.50 0.07 4.00 0.08 4.50 0.09 5.00 0.10 5.50 0.11 6.00 0.12 6.50 0.13 7.00 0.14 7.50 0.15 8.00 0.16 8.50 0.17 9.00 0.18 9.50 0.19 10.00 0.20 10.50 0.21 11.00 0.22 11.50 0.23 (d) Data input and "gures Temperature Data RH Data Pool Data Tmax 25 A 12.5 RH max 95 A 17.5 EL max 95 A 17.5 Tmin 0 Xi 16 RH min 60 Xi 16 EL min 60 Xi 0 Tmean 12.5 RH mean 77.5 EL mean 77.5 Weeks Temp. RH Stress EL 0 0.8 61.1 -5 77.5 1 0.4 60.5 -5 79.6 2 0.1 60.1 -5 81.7 3 0.0 60.0 -5 83.7 4 0.1 60.1 -5 85.6 5 0.4 60.5 -5 87.4 Yearly External Temperature Variation 6 0.8 61.1 -5 89.1 7 1.4 62.0 -5 90.6 8 2.2 63.1 -5 91.9 30 9 3.1 64.4 -5 93.0 25 10 4.2 65.9 -5 93.9 Temperature [oC]

11 5.4 67.6 -5 94.5 20 12 6.7 69.4 -5 94.9 15 13 8.1 71.3 -5 95.0 14 9.5 73.3 -5 94.9 10 15 11.0 75.4 -5 94.5 5 16 12.5 77.5 -10 93.9 0

17 14.0 79.6 -10 93.0 18 15.5 81.7 -10 91.9 0 10 20 30 40 50 19 16.9 83.7 -10 90.6 Time [Weeks]

20 18.3 85.6 -10 89.1 21 19.6 87.4 -10 87.4 (e) Example of provided input data Figure 3.1: Sample of Excel based presentation of results RILEM TC 259-ISR Prognosis of deterioration and loss of serviceability in structures aected by alkali-silica reactions

Bibliography Capra, B. and A. Sellier (2003). Orthotropic modeling of Alkali-Aggregate Reaction in Concrete Structures:

Numerical Simulations. In: Mechanics of Materials 35, pp. 817-830.

Charlwood, R. G. et al. (1992). A Review of Alkali Aggregate Reactions in Hydroelectric Plants and Dams.

In: Proceedings of the International Conference of Alkali-Aggregate Reactions in Hydroelectric Plants and Dams. Ed. by CEA and CANCOLD. Fredericton, Canada, pp. 1-29.

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