Luận án Độ tin cậy chịu uốn của dầm bê tông cốt thép được tăng cường bằng tấm polymer cốt sợi carbon (CFRP)

Name of thesis: “Flexural reliability of RC Bridge girders strengthened with carbon fiber reinforced polymer sheets CFRP” Objectives of this study: to analyze and promote the factor of

BỘ GIÁO DỤC VÀ ĐÀO TẠO TRƯỜNG ĐẠI HỌC GIAO THÔNG VẬN TẢI

NGÔ THANH THỦY

ĐỘ TIN CẬY CHỊU UỐN CỦA DẦM BÊ TÔNG

CỐT THÉP ĐƯỢC TĂNG CƯỜNG BẰNG TẤM POLYMER CỐT SỢI CARBON (CFRP)

CHUYÊN NGÀNH: XÂY DỰNG CẦU HẦM

MÃ SỐ: 62.58.02.05

TÓM TẮT LUẬN ÁN TIẾN SĨ KỸ THUẬT

Người hướng dẫn khoa học:

1 PGS-TS TRẦN ĐỨC NHIỆM

2 PGS-TS NGUYỄN NGỌC LONG

HÀ NỘI - 2015

Luận án được hoàn thành tại: Trường đại học Giao thông vận tải Người hướng dẫn khoa học:

Viện Khoa học công nghệ giao thông vận tải

Luận án sẽ được bảo vệ trước Hội đồng chấm luận án tiến sỹ cấp Trường họp tại: Trường Đại học Giao thông vận tải

Vào hồi: … giờ… Ngày… Tháng… năm 2015

CÁC CÔNG TRÌNH KHOA HỌC ĐÃ CÔNG BỐ

[1] Ngô Thanh Thủy, Độ tin cậy làm việc chịu uốn của dầm bê tông

cốt thép được tăng cường bằng tấm polyme cốt sợi cacbon , Tạp chí Cầu đường Việt Nam – Số 7/2008

[2] Ngô Thanh Thủy, Độ tin cậy làm việc chịu uốn của dầm bê tông

cốt thép được tăng cường bằng tấm sợi cacbon, Đề tài NCKH cấp trường, 3/2012

[3] Ngô Thanh Thủy, Trần Đức Nhiệm, Evaluating Flexural Reliability

of RC Bridge Girders Strengthened with CFRP Sheets Through Statistic Behaviors of Structure and Load, 13th Conference on Science and Technology – International Session, 2013 HCMUT VietNam, Nhà xuất bản xây dựng Hà Nội

[4] Ngô Thanh Thủy, Trần Đức Nhiệm, Huỳnh Xuân Tín, Xây dựng

chương trình tính chỉ số Độ tin cậy làm việc chịu uốn của dầm bê tông cốt thép được tăng cường bằng tấm sợi cacbon , Tạp chí Khoa Học GTVT - Số Đặc biệt 10/2013

INTRODUCTION

Externally bonded fiber reinforce polyme, FRP, has been appeared for 30 years and promptly become one of effective methods in retrofitting old RC structures This method would bring advantages comparing with traditional ones in term of less increasing dead load, unchanging general structures, increasing bending capacity, preventing the appearence of new cracks and widening old cracks in concrete, as well

as easy and faster erection FRP has high tension strength, light weight, good fatigue strength, high corrosion capacity and easily sticking on concrete surface, so that applying FRP in construction has been fast developed over last decades Carbon fiber reinforce polyme, CFRP, receives all advantages of fiber reinforce polyme and has excellent fatigue capacity for retrofitting old bridges, especially RC bridges, more effectively than conventional methods as placing steeel bars in tension zone, externally postensioning cables, or externally bonded steel sheets

Reasons for thesis selection:

CFRP sheets have been used in retrofitting and strengthening bridges in Vietnam; in contrast, current national code for bridges, 22TCN 272-05, has not been designed for CFRP material Some bridges have been designed and erected using ACI 440.2R-08

Researches and calculations for retrofitting and strengthening by CFRP have mostly conducted in semi-reliability method, without considering all statistic behaviours of design parameters Furthermore, other researchs on the world have been using reliability method in several fields However, there is no reaserch completely evaluating the reliability of bending beams strengthened with externally bonded carbon fiber reinforced polymer sheets Thus, reaserch of applying CFRP

basing on reliability theory is a live problem in Vietnam and all over the world This

is the main reason for this thesis selection

Name of thesis: “Flexural reliability of RC Bridge girders strengthened with carbon

fiber reinforced polymer sheets (CFRP)”

Objectives of this study: to analyze and promote the factor of CFRP strength reduction and range of applying externally bonded carbon fiber reinforced polymer

sheets in retrofitting and strengthening RC beams

Methods of this study:

• Theory method: apply reliability theory with possible distributions and statistical parameters of random variables for determining reliability index of bending beams strengthened with externally bonded CFRP sheets

• Experiment method: carry out room and field experiments for getting possible distributions and statistical parameters of random variables in flexural resistance model in ACI 440.2R-08

Subjects and scopes: RC beams strengthened with externally bonded CFRP

sheets

Range of study:

- Suggesting CFRP strength reduction factor and range of applying externally bonded carbon fiber reinforced polymer sheets in retrofitting and strengthening RC beams

• Experiment: define possible distributions and values of statistical parameters

of random variables, icluding section geometry, concrete compressive strength, steel yield strength, and influence of analysis method to flexual resistance of RC beams strengthened with externally bonded CFRP sheets according to ACI 440.2R-08 basing on bending sample beams to rupture

Terms of rasearch include introduction, 4 chapters, and conclusions as following:

Introduction: Introduction of CFRP sheets and name of thesis

• Chapter 1: General view of reaserchs about structures using FRP

• Chapter 2: Analyzed reliability index, β, of RC beams strengthened with externally bonded CFRP sheets according to bending resistance model in ACI

440.2R-08

• Chapter 3: Studying RC sample beams strengthened with externally bonded

CFRP sheets throught bending to failure

• Chapter 4: Studying Trần Hưng Đạo bridge beams strengthened with

externally bonded CFRP sheets under bending with calibrated loads

Conclusions and suggestions: presenting results, suggestion, and proposed

topics for future researches

Chapter 1 GENERAL VIEW OF RESEARCH ABOUT STRUCTURES USING FRP 1.1 History of applying FRP in retrofitting and strengthening structures

Reinforce concrete bridges are popular in Vietnam and all over the world Nowadays, there are many serious deteriorations, however, there is not enough budget for replacing with new ones so retrofitting and strengthening bridges seem to be the best choice Strengthening methods are varied depending on demand, structure, and e technical level According to statistic, bridge strengthening is mainly using conventional methods as placing steeel bars in tension zone, externally postensioning cables, or externally bonded steel sheets

Externally bonded FRP has been appeared for 30 years and promptly become one

of effective methods in retrofitting old RC structures This method would bring advantages comparing with conventional ones in term of (1) less increasing dead load, (2) unchanging general structures, (3) increasing bending capacity, (4) preventing the appearence of new cracks and widening of old cracks in concrete, and (5) easy and fast erection FRP has high tension strength, light weight, good fatigue strength, high corrosion capacity and easily sticking on concrete surface, so that applying FRP in construction has been fast develope over last decades

In 1980s, the first time FRP was applied for retrofitting RC columns in Japans In Euro, as early as 1978, German researches had been mentioned the issue of using FRP

in strengthening RC structures Similarly, Switzer researchers had applied FRP for strengthening bridge beam in bending in 1987 In The USA, applying FRP was researched as early as 1930s, but the using of FRP in retrofitting and strengthening has been started in 1980s

In Vietnam, FRP has been applied in strengthening bridges as: Sài Gòn-HCM city; Trần Hưng Đạo - Phan Thiết city, Bình Thuận province; Trần Thị Lý- Đà Nẵng city, Gián Khẩu- Ninh Bình province, Tô Mậu - Yên Bái province

1.2 FRP mechanical properties

Unit weight of FRP is from 1.2 g/cm3 to 2.1 g/cm3, about 1/4 to 1/6 that of steel Unidirectional FRP has different

thermal coefictions for longitudinal and

transver directions depending on type of

fibers, matrix, and volume of fiber

FRP in tension has linear

relationship between stress and strain

until rupture and this is truely a brittle

material (Figure 1-1) FRP mechanical

properties decrease under the impact of

environment factors including: high

temperature, humidity, and chemicals

Figure 1-1 Relationship between typical

FRP stress and strain

1.3 FRP application

Main FRP application includes: retrofitting and strengthening structures; reinforcing for RC; and constructing main frame

1.4 Existing design manual for FRP

1.4.1 Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures

Design bending RC section strengthening with externally bonded FRP base on beam theory with reinforce addition of FRP combining for tension Acorrding to ACI 440.2R-08, flexural expression at limit state is as following:

∅M+ ψM ≥ γM+ γ M

1.4.2 Externally bonded FRP reinforcement for RC structures-FIB Bulletin No

14

Design bending RC section strengthening with externally bonded FRP acorrding

to FIB is similar to that of ACI:

= "# −$!% + "&'#ℎ −$!%

1.5 Structure Reliability

1.5.1 Basic of Reliability theory

Probability of Stable, Ps: P S = P{S<R | [0,T]}

and probability of failure: P f = P{S>R | [0,T]}

where P{S<R | [0,T]} is the probability for structure not break-down during

operation time, T; P{S>R | [0,T]} is the probability for structure break-down during

This is a modern design method; taking into account for unstable and random characteristics of design variables However, it is needed to get enough Possible Distributions and Statistical parameters of all variables

strengthened; or Designing strengthening RC structures with given reliability

Methodology for Evaluating the reliability of RC structures being strengthened base on basic reliability theory Widely accepted model for design is beam theory with the addition of CFRP as part of tension material

For given reliability, β, probability of structure fail is defined With analyzed model and design beam parameters specified, all demands of FRP are established

1.5.2.2 Possible distributions and values of statistical parameters of random

variables

with externally bonded CFRP sheets

Reliability of RC bending beams strengthening with externally bonded CFRP

sheets depends on many elements such as: design standards, design level,

construction technology, management and operation, loads, and environment Evaluating the reliability of RC structures being strengthened with externally bonded CFRP sheets is only used to deal with random variables having specified statistical parameters and describing their influence to structure reliablity through state functions

1.5.3 Reliability index, β

1.5.3.1 Definition of Reliability index, β

Figure 1- 2 Diagram of state function for Resistance, R,

Load effect, S, and safty reserve, G

Ratio of ( =)*

+ * is called Reliability index of structures

Reliability index is computed through means and standard deviations of Resistance, R, and Load effect, S as ( = ), -).

Target Reliability index selected depends on influence level to social when structures are broken Target Reliability index is different from new and strengthened structures

human-economy-Research Andrzej S Nowak, Maria M Szerszen, and Allen; together with regulations of ASSHTO LRFD, EC, ACI 318- 05, Target Reliability index is proposed in this thesis as following:

• βT = 3.75: multiple paths beam structures, strengthening age of 10 years

• βT = 3.5: multiple paths beam structures, strengthening age of 5 years

This method is based on equivalent mean and standard deviation of variables with unnormal distribution Susposing random variable, X, has mean of µX; standard deviation of σX; distribution function of FX(x) and density distribution function of

fX(x) Equivalent mean of µ34 and standard deviation of σ34 is defined at point x*

where values of FX(x) and fX(x) are repectively equal to those of distribution function and density distribution function of standard normal distribution Point x* is on the limiting line or G=0

standard deviation of σ34 is defined as following:

µ34 = x∗− σ34@8-F3x∗A σ34 =;:∗φ@8-F3x∗A Iteration method is used for determining x* and β

1.5.4 Analyis of statistic parameters

Minimum sample size, Bmin, of material, X, having covariance, COVX, approximate constant compared with mean, µX, is defined as following: BCD=

fECOVI/e !

Checking random variable, X, with a set of B samples for appropriating with normal distribution includes:

• Graphs (lines or colums for prbability distribution);

• Checking synmetry value of Fisher, g1, and kurtosis value of Pearson, g2

• Using standard Wilk for sets of 3 to 20 samples; or extended Wilk with Royston algorithm for sets of 20 samples or more

Shapiro-1.6 Analyze, evaluate research about beams strengthening with CFRP sheets

In general, researches from all over the world to Vietnam have been studied beams strengthening with externally bonded CFRP sheets about many issues, including:

• Type of failure

• Ultimate strength capacity

• Section Stress Distribution

• Advantages of FRP external bonded method for bending and shear

• Model for evaluating peeling of CFRP sheets

• Finite Element Model for evaluating beams strengthening with externally bonded CFRP sheets

• Using ductility index to evaluate beams strengthening with externally bonded CFRP sheets

Terms of research are various but all of them are conducted in semi-reliability method, not implying all statistic behaviours of design parameters

1.7 Analyze, evaluate researches about reliability theory

In general, researches from all over the world to Vietnam have been applied reliability theory in many issues, including:

• Avaluating beam element

• Factors of loads and resistance

• GFRP bar reinforcement for concrete

• Beam with large ratio of reinforcement

• Bridge deck at service limit state

• Box-section RC beams

These researches have been using reliability method in several fields However, there is no reaserch completely evaluating the reliability of bending beams strengthened with externally bonded carbon fiber reinforced polymer sheets

1.8 Objects of thesis

Evaluating influences of materials, geometry, and analysis model of bending resistance to reliability of beams strengthening with externally bonded CFRP sheets Evaluating and suggesting application range of strengthening with externally bonded CFRP sheets for single span beams and CFRP strength reduction factor

1.9 Terms and Methods of this study

Computing and evaluating reliability index of bending beams strengthened with externally bonded CFRP sheets; suggesting application range of strengthening with externally bonded CFRP sheets and CFRP strength reduction factor

Theory method: applying reliability theory with possible distributions and statistical parameters of random variables for determining reliability index of bending beams strengthened with externally bonded CFRP sheets

Experiment method: carrying out room and field experiments for getting possible distributions and statistical parameters of random variables in flexural resistance model in ACI 440.2R-08

Chapter 2 EVALUATING FLEXURAL RELIABILITY INDEX OF RC BRIDGE GIRDERS STRENGTHENED WITH CFRP SHEETS BASING ON FLEXURAL

RESISTANCE MODEL OF ACI 440.2R-08

• Reliability index, β, of bending sections of RC bridge girders strengthened with carbon fiber reinforced polymer (CFRP) sheets has been computed according to ultimate limit state (ULS) for flexural design suggested by the ACI 440.2R-08 2880 strengthened RC beam-sections have been selected with reasonable sets of random variables (section dimensions, concrete compressive strength, steel strength, ultimate strength and ultimate relative strain of CFRP sheets) applying in analyzing model of nominal flexural resistance, ML Monte-Carlo simulations have been performed to determine the variability in material properties (M) and fabrication processes (F); whereas experimental data reported in the literature has been used to quatify the variability related to the analysis method (P) The reliability index, β, caculated using

Rackwitz-Fiessler method with first order function

2.1 Statistical properties of section geometry and materials

• Geometrical properties: width of section, b, can be measured easily after construction, so that two extreme nominal values λ were selected 1.01 and 1.00; and

two values COV were selected as 1.78% and 0.60%, respectively (Table 2-1) The

effect of concrete vibrators to the positions of tension steel could hardly to measure after construction, thus two extreme nominal values λ of d were selected as 0.99 and 1.00, respectively; and two values COV of d were selected as 2.36% and 0.78%,

respectively (Table 2-1) h values are proportionally related to d Both b and d are

assumed to have Normal distribution

• Concrete Compressive Strength, M′, is closely related to construction level and

curing The bias at sites is usually smaller than in lab and the suggested value is 1.05 Two nominal values COV of grade 17 and 30 were selected: 15% and 13.5%, respectively Compressive strength of concrete is assumed to be normally distributed

• Tensile Strength of steel bars, : two types of steel and their extreme nominal values

of  were considered in Table 2-1 Selected bias value is 1.10, near the lower limit;

Selected COV value is 10%, near the upper limit  is assumed to be normally distributed E= 200000MPa

• Tension strength, fR∗ , and limit relative strain, εR∗ , of CFRP is selected in

value of tension strength is 12% ,near the upper limit Selected COV value of limit relative strain is 2.5% , near average value These variables are assumed to agree with Weibull distribution FRP modulus of elasticity: E= 230000MPa

2.2 Design space

So that design space of section resistance includes 24 x 3 x 5 = 240 cases

Table 2-1 Statistical Properties of Main Variables

j & k & COV Bias λ

(%)

Probability Distribution

2.3 Influenced factors for flexural resistance:

Flexural resistance, MR, is a random variable and according to Ellingwood, 2003 [9], the factors influenced to flexural resistance random characteristic include:

• Material properties (M): strength, modulus of elasticity, relative strain…

• Fabrication (F): dimensions and their effects to geometric properties

• Analysis method (P): accurate level of selected method in ACI 440.2R-08

M, F and P are assumed to be independent variables Effects of M and F are evaluated together through values of λMF and COVMF These values are computed by randomly generated variables of material properties and fabrication as Monte Carlo simulation

Effects of P is evaluated by comparing experimental values of the flexural capacity available

in literature, t,xyz with the corresponding analytical value {|}, derived using the analysis

method proposed by ACI 440.2R-08 (Table 2-2).The following values were chosen: ~=

€  and ‚ƒ„= €…%

Table 2-2 Statistical Properties of P

2.4 Load model

Dead load (D) and live load (L) are the two load categories considered in this study

The dead load considered in the design is the gravity load due to the self weight of the structure It is normally treated as a Normal random variables in literature (Cardoso et.al,2007, Nowak 1993-1995-1999 and Project No NCHRP 20-7/187 - ASSHTO 2007); because of the control over construction materials, it is assumed that the accuracy to estimate dead loads is higher compared to that of live loads The works in this study induced to adopt a bias ~‹=

€ …Œ V ‚ƒ„‹= €…% for dead load

In this study, live load is HL 93 and its statistical properties are available in Project No NCHRP 20-7/187 - ASSHTO 2007 Live load is assumed to agree with Gumbel distribution In this study, Ž=1.20 and COV L =18% are selected

2.5 Evaluating reliability index

2.5.1 State function:

State function to determine flexural reliability index β based on ACI 440.2R-08 concludes 3 random variables: flexural resistace, MR, dead load moment, MD, and live load moment, ML: GML, M, M ,  = ML− M+ M 

Assuming ratio of live load moment to dead load moment at specific section is n’ =’“

2.5.2 Computer aided software

1.8 Objects of thesis

Evaluating influences... and Methods of this study

Computing and evaluating reliability index of bending beams strengthened with externally bonded CFRP sheets; suggesting application range of strengthening with... Reliability index, β, of bending sections of RC bridge girders strengthened with carbon fiber reinforced polymer (CFRP) sheets has been computed according to ultimate limit state (ULS) for flexural