Moisture Diffusion and Long-term Deformation of Concrete KAIST Civil and Environmental Engineering Jin-Keun KIM

Moisture diffusion of concrete Prediction of long-term deformation Index Moisture diffusion of concrete Prediction of long-term deformation Researches in KAIST

Moisture diffusion of concrete Definition of the diffusion Diffusion is the net movement of a substance (e.g., an atom, ion or molecule) from a region of high concentration to a region of low concentration. This is also referred to as the movement of a substance down a concentration gradient.

Moisture diffusion of concrete Fick’s first law of diffusion J : diffusion flux D : diffusion coefficient or diffusivity (m2/s) c : concentration For steady state, For unsteady state,

Moisture diffusion of concrete Moisture diffusion equation For pore relative humidity Diffusion coefficient For pore moisture content

Moisture diffusion of concrete The effect of relative humidity and temperature on the diffusion coefficient Relationship between relative humidity and diffusion coefficient Relationship between temperature and diffusion coefficient

Moisture diffusion of concrete Moisture diffusion coefficient suggested in CEB-FIP(‘90) For isotherm condition D1 : diffusion coefficient when h = 1.0 D0 : diffusion coefficient when h = 0 : D0 /D1 hc : diffusion coefficient when D (h) = 0.5D1 n : exponent h : pore relative humidity D1,0 = 3.6 10-6 (m2/hr) fck0 = 10 MPa fck = fcm-8 MPa

Moisture diffusion of concrete Moisture diffusion coefficient suggested by Bazant ( 0.75)

Moisture diffusion of concrete Moisture diffusion coefficient by Mihashi D1 : diffusion coefficient at saturated condition (h=1) and 20oC U : activation energy R : gas constant , hc, n, N1, N2 : material constants depending on the mixture and curing condition

Moisture diffusion of concrete Boundary condition : environmental humidity : surface humidity Surface factor equation suggested by Sakata Equivalent thickness by Bazant around 0.75 mm

Moisture diffusion of concrete Moisture diffusion of concrete → Change of internal humidity ⇒ Change of mechanical properties : Compressive strength, Modulus of elasticity Change of long-term deformation : Creep and shrinkage Differential drying shrinkage ⇒ shrinkage crack

Differential drying shrinkage Cause moisture content difference at every position in the concrete by the moisture diffusion

Compressive strength (MPa) Cement content (kgf/m3) Differential drying shrinkage - example Slab Analysis parameters - Fixed end, Free end - Thickness (h) : 0.2, 0.4, 0.8 m - Ambient humidity : 30, 50, 80 % Concrete Compressive strength (MPa) 24 Cement content (kgf/m3) 300 Water content (kgf/m3) 180 Free end Fixed end

Differential drying shrinkage - example Humidity versus depth of slab – Ambient humidity is 30% H = 0.2m H = 0.4m H = 0.8m

Differential drying shrinkage - example Humidity versus depth of slab – Ambient humidity is 50% H = 0.2m H = 0.4m H = 0.8m

Differential drying shrinkage - example Humidity versus depth of slab – Ambient humidity is 80% H = 0.2m H = 0.4m H = 0.8m

Differential drying shrinkage - example Stress versus depth of slab – Ambient humidity is 30% H = 0.2m H = 0.4m H = 0.8m

Differential drying shrinkage - example Stress versus depth of slab – Ambient humidity is 50% H = 0.2m H = 0.4m H = 0.8m

Differential drying shrinkage - example Stress versus depth of slab – Ambient humidity is 80% H = 0.2m H = 0.4m H = 0.8m

Differential drying shrinkage - example Strain versus time – Free end Ambient humidity : 30% Ambient humidity : 50% Ambient humidity : 80%

Differential drying shrinkage - example Stress versus depth of slab – Ambient humidity is 30% H = 0.2m H = 0.4m H = 0.8m

Differential drying shrinkage - example Stress versus depth of slab – Ambient humidity is 50% H = 0.2m H = 0.4m H = 0.8m

Differential drying shrinkage - example Stress versus depth of slab – Ambient humidity is 80% H = 0.2m H = 0.4m H = 0.8m

Importance of prediction of long-term deformation Column shortening in high-rise building Prestress loss in the PS structures Long-term deformation in beam and slab Expansion and reduction of the crack width Re-distribution of stress between steel and concrete in RC member

Researches in KAIST Autogenous shrinkage and basic creep Creep of concrete under multi-axial stresses Differential drying shrinkage Study on column shortening

+ Autogenous shrinkage and basic creep Existing basic creep model high strength and/or early age concrete elastic + creep deformation + autogenous shrinkage autogenous shrinkage separation from basic creep model Basic creep of concrete is creep deformation produced under applied stress without moisture migration to the atmosphere. Autogenous shrinkage of concrete is a phenomenon that concrete contracts itself without change of weight and temperature of concrete. Basic creep strain measured from conventional basic creep test contains autogenous shrinkage. So current basic creep model based on conventional basic creep test data contains elastic and creep deformation dependent on applied stress, and autogenous shrinkage. Whether this autogenous shrinkage depends on applied stress or not will be revealed in this study. Up to now this autogenous shrinkage has been ignored in basic creep model. In case of ordinary strength concrete or hardened concrete, autogenous shrinkage is small, so current basic creep model is applicable to these kinds of concrete. But nowadays, the use of high strength concrete whose autogenous shrinkage cannot be ignorable increases in construction sites. So, to develop a basic creep model applicable to high strength or early age concrete, this autogenous shrinkage has to be separated from current basic creep model. So the objective of this study is to show the necessity of a new basic creep model considering autogenous shrinkage effect on basic creep model. Applicability of basic creep model should be checked !

Autogenous shrinkage and basic creep Test 1 : Autogenous shrinkage and basic creep test for various w/c ratios Tested for four different types of concrete mix Variables autogenous shrinkage test : w/c ratios - 30, 40, 50, and 60% basic creep test : w/c ratios - 30, 40, 50, and 60% : loading ages - 1, 3, 7, and 28 days Concrete mix proportions W/C (%) unit weight (kgf/m3) Ad W C S G 30 175 583 591 999 1.0% 40 438 687 1031 0.6% 50 350 752 0.3% 60 292 849 1030 0.1% Next I’ll talk about test program performed in this study. To obtain previously mentioned real basic creep, autogenous shrinkage and basic creep test for various W/C ratios were performed in this study. Test was performed for four different types of concrete mix. Test variable of autogenous shrinkage test is water cement ratio such 30, 40, 50 and 60%. Test variable of basic creep test is water cement ratio, and loading ages, This table shows concrete mix proportions for four water cement ratios.

Autogenous shrinkage and basic creep Test 2 : Autogenous shrinkage and basic creep test for various applied load Tested for w/c ratio 30% at 1 day age Variables basic creep test : applied load levels – 0.1, 0.2, 0.3, and 0.4fc’ In this study, autogenous shrinkage and basic creep test for various applied load were performed to verify the applicability of basic creep model and effect autogenous shrinkage on basic creep of concrete. Test was performed for water cement ratio 30% at 1day age. Test variable of basic creep test is applied load levels such as 10, 20 ,30, and 40 percent of compressive strength of concrete at 1day. In autogenous shrinkage test, prism and cylinder specimens were used as shown in this picture. There were no remarkable differences of autogenous shrinkage between two cases. In basic creep test, four applied load were measured from each load cell equipped to each testing device as shown in this picture. Autogenous shrinkage test Basic creep test for four stress levels

Autogenous shrinkage and basic creep Autogenous shrinkage test Autogenous shrinkage drastically increases at early ages. Early age stage Hardening stage Next I’ll talk about the test results. This graph shows autogenous shrinkage strains for four water cement ratios. From this figure, we can see that autogenous shrinkage increases as water cement ratio decreases and the amount of that is remarkable especially for water cement ratio 30%. Measured autogenous shrinkage strains

Autogenous shrinkage and basic creep Apparent and real basic creep autogenous shrinkage from t’ to t elastic strain real basic creep apparent basic creep Next I’ll introduce apparent and real basic creep defined in this study. This figure shows basic creep strain measured from basic creep test under applied stress sigma zero loading at age t’. In this study apparent basic creep is defined as total strain measured from basic creep test shown as this line in this figure. So this apparent basic creep contains elastic, creep, and autogenous shrinkage strain. On the other hand, real basic creep shown as this line can be obtained by excluding autogenous shrinkage from apparent basic creep. .

Autogenous shrinkage and basic creep Basic creep test for various w/c ratios The difference between real and apparent creep compliance function is clearly visible in case of loading at 1 and 3 days. t’ = 1 day t’ = 1 day t’ = 3 days t’ = 3 days t’ = 7 days t’ = 7 days t’ = 28 days . t’ = 28 days Next I’ show test results of basic creep test for four water cement ratios. This is the case of water cement ratio 30%, this is for 40%. In this graph, black line means apparent basic creep compliance, and red line means real basic creep compliance obtained from previous method. From these results we can see that the differences between real and apparent creep compliance are obvious in case of loading at 1 and 3 days. Apparent and real basic creep compliance functions with age

Autogenous shrinkage and basic creep Basic creep test for four applied load levels t’ = 1 day, W/C = 30% fc’ = 23MPa t’ = 1 day, W/C = 30% fc’ = 23MPa . This is test results of basic creep test for four applied load levels. This figure shows total strain including autogenous shrinkage, and this figure shows total strain excluding autogenous shrinkage. Total strain including and excluding autogenous shrinkage

Autogenous shrinkage and basic creep The comparison of apparent and real basic creep Real basic creep can be obtained from conventional basic creep tests by simply subtracting the autogenous shrinkage in a stress-free state. This graph shows total strain excluding autogenous shrinkage with applied load. In this graph, this red line passing through the origin and this point passes other two points. This means this real creep compliance is independent on applied stress. So this equation is true. On the other hand, we can see that these three points have linear relationship in previous and this graph. This means autogenous shrinkage is independent of applied stress. From these conclusions, we can see that this equation using real creep compliace is true ! Apparent and real basic creep compliance functions with age

Creep of concrete under multiaxial stresses Concrete is generally subjected to multiaxial stresses in many structures. Multiaxial Stress Uniaxial Stress 매스콘크리트, 원자력 격납구조물의 이방향프리스트레스 부재, 내진설계에 의해 횡보강재가 많이 사용된 기둥 등 많은 구조물에서 콘크리트는 다축응력 상태에 놓이게 됩니다. 기존의 연구는 일축응력상태를 대상으로 크리프 특성을 규명하고자 하는 데 치중했으며, 메커니즘, 수학모델, 예측모델 등의 개발이 이루어져왔습니다. 그러나 다축응력 상태에 대한 연구는 매우 부족했으며, 연구결과들도 서로 일치하지 않아, 다축응력 상태의 크리프 특성은 아직까지 명확히 규명되어 있지 않습니다.

Creep of concrete under multiaxial stresses Experimental apparatus 이 그림은 2축응력과 3축응력을 가하지 위해 제작된 실험장치를 나타낸 것입니다. 일정한 하중을 유지하기 위해 유압펌프, 유압게이지를 전자제어장치에 연결하여 시간에 따라 실린더 내에 일정한 유압이 작용하도록 하였습니다. Biaxial stress state Triaxial stress state

Creep of concrete under multiaxial stresses Creep Poisson’s ratio CI CII CIII 초기의 급격한 변화는 실험결과에 민감하기 때문이다. 0.15~0.20사이로 분포 fluctuation of creep Poisson’s ratio with time, it is difficult to distinguish whether these values are increasing, decreasing or remaining constant with time. Time(days)

Creep of concrete under multiaxial stresses Effective creep Poisson’s ratio CI CII CIII 삼축응력 상태의 effective Poisson’s ratio가 이축응력상태의 포아송 비보다 작게 나타났으며, CI 콘크리트의 경우 CII, 와 CIII 콘크리트에 비 작은 값을 보였습니다. 전체적으로 about 0.16 to 0.2. Time(days)

Creep of concrete under multiaxial stresses Volumetric components of stress and creep strain CI CII CIII Multi-axial creep deformation of concrete under multi-axial stresses can be interpreted in terms of the superimposed volumetric and deviatoric components of strain and stress. This figure shows the volumetric stresses and creep strains at 1, 4, 7, 28 days after initial loading. The volumetric stresses and strains were obtained from these equations. The volumetric stresses were linearly proportional to volumetric creep strains and the linear relationship remained with time. It can be shown that the volumetric stresses and creep strains had the same relationship even though the stress combinations applied to the specimens were different.

Creep of concrete under multiaxial stresses Deviatoric components of stress and creep strain CI CII CIII This figure shows the relationship between deviatoric stresses and deviatoric creep strains. The deviatoric stresses and the deviatoric creep strains also had the linear relationship. The linearity of volumetric components and deviatoric components remained with time and multi-axial creep can be analyzed with this linear property. In second analytical study, this linearity will be used.

Differential drying shirnkage Measurement of RH Specimen

Differential drying shirnkage Experimental results Relative humidity at each point with time (t0 = 3 days) w/c = 0.28 w/c = 0. 40 w/c = 0.68

Differential drying shirnkage 부등건조수축 Differential drying shirnkage Experimental results Relative humidity at each point with time (t0 = 28 days) w/c = 0.28 w/c = 0. 40 w/c = 0.68

Differential drying shirnkage 부등건조수축 Differential drying shirnkage Experimental results Shrinkage strain at each point with time (t0 = 3 days) w/c = 0.28 w/c = 0. 40 w/c = 0.68

Differential drying shirnkage 부등건조수축 Differential drying shirnkage Experimental results Shrinkage strain at each point with time (t0 = 3 days) w/c = 0.28 w/c = 0. 40 w/c = 0.68

Importance of the study Study on column shortening Importance of the study Differential column shortening Serviceability and safety problems Demands for reasonable prediction of shortening Crack Distortion of wall Exterior column Interior column Deformation of anchor of elevator

Needs of prediction of column shortening in SRC columns Study on column shortening Needs of prediction of column shortening in SRC columns

Characteristic of SRC columns and analysis procedures Study on column shortening Characteristic of SRC columns and analysis procedures d𝜀 𝑠ℎ = 𝑘 𝑠ℎ dℎ 𝜀 𝑠ℎ : drying shrinkage ℎ : relative humidity at a point in the section H1 H2 H1 > H2 H3 H4 H3 < H4 H : Relative humidity 𝑘 𝑠ℎ = 𝜀 𝑠 0 𝑔 𝑠 (𝑡) d 𝑓 𝑠 (ℎ) d ℎ : ultimate shrinkage 𝑓 𝑠 (ℎ) = 1− ℎ 3

Study on column shortening Analysis program Analysis of moisture diffusion Relative humidity distribution in concrete Calculate initial strain and curvature at time 𝒕 𝟎 Calculate free shrinkage strain and creep strain at each location of concrete Calculate the restraining stress Calculate the restraining resultants Calculate the strain at a reference point 0 and curvature at time t Calculate the strain at each location and stress at time t

Differential drying shrinkage analysis result Study on column shortening Differential drying shrinkage analysis result 60cm each side, covering depth 10cm w/c = 0.3 Environmental condition : 20℃, 65% Plain H Cross

Study on long-term deformation depending on the finishing materials Study on column shortening Study on long-term deformation depending on the finishing materials w/c = 0.3 Environmental condition : 20℃, 40% Finishing material : oil-paint, water-paint, waterproofer [Drying shinkage] [Creep]

Study on column shortening Gradual development of the global stiffness matrix sequence 1

Study on column shortening Gradual development of the global stiffness matrix sequence 1 sequence 2

Study on column shortening Gradual development of the global stiffness matrix sequence 1 sequence 2 sequence 3

Study on column shortening Gradual development of the global stiffness matrix sequence 1 sequence 2 sequence 3 sequence 4

Study on column shortening Gradual development of the global stiffness matrix sequence 1 sequence 2 sequence 3 sequence 4 sequence 5

Study on column shortening Gradual development of the global stiffness matrix sequence 1 sequence 2 sequence 3 sequence 4 sequence 5 sequence 6

Study on column shortening Result of column shortening analysis C214 C216 C236 Modeled part Overall trend of analysis result coincide with measured data Because of the lack of construction information and accuracy of measurement, errors exist.

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