飛来塩分シミュレーションおよびコンクリート内拡散モデル[Aerosol Chloride Simulation & Chloride Ingression Model]
岡村

甫 1、Swatekititham Supakit2

高知工科大学 社会システム工学科
782-8502 高知県香美市土佐山田町宮ノ口 185

Abstract
According to the Japan Coastal scenery, the variety of chloride attacks by typhoon in the Pacific Ocean
induced aerosol chlorides formation along east coast and windy condition in winter season along JapanSea coastline. Many structures were detected the damage due to chloride attack on bridge structures
constructed in land. Dealing with this problem, a systematic life-span simulation limited by the initiationof steel bars corrosion is established for the structural degradation. The degradation of bridge structures isdue to the aerosol chlorides ingression in concrete induced corrosion and crack. Thus, the mechanism ofaerosol chlorides formation, transport and ingression in concrete is systematically purposed by taking theenvironmental loads, structural layout and concrete properties into account. During typhoon periods, thewave height and wind speed are dramatically large which results to a large amount of aerosol chlorides
transported to the structural members at a long distance. 2-D sea salt aerosol (SSA) particles withheight-distance distribution are proposed at the wave breaking location. The SSA particles for theproducts generally contain the distribution in the range of 1-300µm diameter. SSA particles transport
along-wind flow considering the gravitational sedimentation and turbulent vertical eddy diffusivity. SSA
particles are transported and accumulated on the surface of structure. Rain effect on the surface chloride
dissolution on the front girder and along rain drainage path is also taken into account. The SSA
penetration in concrete is referred to the Fick’s 2nd Law of diffusion. If the limitation of chloride thresholdat the steel bars position were defined, the initiation of steel bars corrosion for each member would bepredicted. This model aims to predict the performance of the existing structures in Japan and to estimate
the serviceability for any structures.

Introduction
The sustainability in design is therefore
important for asset management on theoptimization of materials, total cost against
withlong-lifeserviceability.
The
performance-based simulation and design
contributes to the life-span prediction of astructure under severe environment. The
performance-based simulation of bridge
structures under marine environment ismentioned in this research. The analysis ofstructural deterioration is depending on theprocess of aerosol chloride formation andtransportation, aerosol chloride ingression,
steel bars corrosion and rust induced crack,respectively. The research is divided into
three categories, 1) aerosol chloride

formation at the seashore, 2) aerosol chloride
transportation, and 3) chloride ingression inconcrete [3,5].

Model of Life-span Simulation
1) Aerosol chloride formation at theseashore
The first step of systematic simulation starts
with the aerosol chlorides formation. The
weight of airborne chlorides is presented in aheight distribution according to four main
parameters of breaking wave height, windspeed, wind directions and breakwater.
However, the breaking wave height at thesurf zone is calculated based on the wave
transformation from the transition zone toseashore. The wave height transformationand the energy dissipation in the shallow
water zone play the necessity to define thewave height during breaking. Plenty ofmodels on wave transformation werepurposed in singular wave approach andspectral wave approach. In this paper, thesingular wave approach which means asinusoidal wave with the significant wave
height (H1/3) is applied. H1/3 commonly
represents the wave height as provided by theJapan Meteorological Agency (JMA). Thewave energy conservation is applied toexplain
themechanismofwave
transformation in this paper as shown [1-3],∂(E.cg cosω − E f − Et )∂xi= −DB(1)where, E is the wave energy density, cg is thegroup velocity which is proportioned with thewave phase speed, ω is the mean wave
diffraction angle, x is the distance in crossshore direction, Ef is friction energy loss, Et istearing loss and DB is the energy dissipation
rate in the surf zone.
The amount of airborne chlorides generated
at a low level is large and decreases in a highlevel. A proper method is to propose theaerosol chlorides distribution in the air by thepower function as;
(2)

(3)
(4)
where, Wh(t) is hourly aerosol chloride content(mg/dm2/hr). hair is the reflected height fromground (m). U is wind speed at 10m height at
seashore. a is particles dispersion factor. b isamount of droplets on ground. Hb is breaking
wave height (m) calculated by the wave
propagation. γ is salt concentration ratio = 1.0 at
3% salt concentration. α1 is the functional height
coefficient (~0.7). α2 is 1.0 if none of breakwater
is involved. α3 is 0.75 for sandy beach. rwind is 1.0
if a wind direction could transport the airborne
particles from seaside, otherwise it is defined asnull. T is sea surface temperature (°c) affecting
sea surface viscosity.

Breaking wave starts from wave crest andincreases to overall breaking while it isentering the shoreline. The weight of aerosol
chlorides in x-distribution is proposed as aproportional to the area under the standard
normal distribution (Ndist) and the distance ofwave breaking initiation (x’) is assumed z =-3.0. At breaking of wave, SSA size
distribution has also commonly been reported
that none of formulation is standardized. In
this paper, the particle size distribution isidealized as circular relation with the spume
drops (di) in the size range 0-300 µm. Total
distribution of aerosol chloride content isillustrated in Fig.1.

Fig.1. Superposition method for aerosol chlorides formation with height, distance and particle
sizes distribution (di = 0-300 µm) by wave breaking and breakwater

2) Aerosol chloride transportation [5]In this paper, only spume droplets are
mentioned on the influence to the chloride
attack of structures. The spume droplets arelarge in size which the sedimentation is rather
important than the particles diffusivity. The
mass equilibrium of each particle is proposed
in 2-dimensional free space movement
including the eddy diffusion from theturbulence of wind flow as shown in Eqs.5-6.
The aerosol chlorides transport is modeled bysimulating the movement of an individual
particle. The total amount of aerosol
chlorides at a certain height and distance(Wh,x) can be obtained by integrating theamount of all particle sizes by Eq.7.

(5)
(6)
(7)

where, Wd,h,x is weight of aerosol chlorides
formed in a height and distance of a single
particle size (µg/m2/sec). v is vertical velocity(uplifted velocity – terminal velocity), which
the terminal velocity of particles werepurposed by Clift et al [18]. The
compressible wind flux in a specificlandscape can be computed by theNavier-Stoke’s Equation. U and v could be
simply assumed a constant value forfree-space simulation. Deddy is eddy
turbulence represented by eddy diffusion
coefficient (dm2/s) which depends on particle
size. In the surface layer, the dominantstresses are due to turbulence and are nearly
independent of height; Deddy is referred to as
the constant value with height of a few tensof meters. According to the individual
particle movement assumption, the degree ofeddy diffusion is related with the particles
size diffuse in the air (bigger particle, larger
chloride ions composition). Wh,x is total
weight of aerosol chlorides at a certain heightand distance from seashore. ζ is the SSA
reduction factor due to the deposition on theobstacles along the transportation path. η isthe coefficient of SSA deposition on astructural member due to structural shape.
The girders and slab surfaces might not havethe same amount of SSA deposition due tothe wind stream path under the bridge. Vortex
streets might be one of the factors to cause
the variation of SSA deposition. The windflow characteristic passing under the bridge
is varying with the girder height (hg) to slab
span (w) ratio. The obstacle and structuralmember impacts on the deposition of SSA
particles are neglected in this paper (ζ and η=1.0), because the mechanism is still
unknown.
3) Chloride ingression in concrete
The aerosol chlorides transported to surfacesof structural members ingress into concrete
time-dependently described by Fick’s 2nd
Law of diffusion. The aerosol chlorides
transported to the structure member which iscalculated from above models, is the initialchlorides penetrating through concrete. The
free chlorides flux movement penetrated into
concrete by diffusion and advection. For
indoor structures, the advection flux of bulk
water movement is neglected due to thegradually change of saturation in concrete.
During raining, the surface chloride isdissolved with the drainage flow. Rain causes
the reduction of the total surface chlorides
ingress in concrete and prolongs the steel
bars corrosion time. Thus, rain or waterflushing method on the structure might be asimple method to prolong the structural life.
This statement can be proved by the chlorides
diffusion equation including rain effect asfollows,

(8)

(9)
(10)
(11)

where, Cfree(x,t) is free chloride concentration
at a distance x and time t (mol/l). F(x,t) isflux of free chlorides movement. D(t) isdiffusion coefficient of free chloride(cm2/day). Dcl is diffusion coefficient ofchloride ions in pore water (=0.0259cm2/day].
φpore is ratio of pore volume in a unit ofconcrete. S is degree of saturation (=1.0 forsaturated pore). Tk is concrete temperature(°c) which affects to the diffusivity as
referred to the Arrhenius’s Law. F(0,t) is flux
from aerosol chloride adsorption on concretesurface. Free chloride concentration could becomputed as referred in Maruya et al [6].
Cfree(0,t) is the amount SSA on surface ofconcrete (Wh,x) or the dissolution of surface
chlorides by rain which is -1.9x10-6 mol/l.day[4] at a specific time.
Experimental WorkIn the simulation, the environmental data ofwind and wave in year 2003 from Japan
Meteorological Agency; JMA is represented
as annual cycle of hourly inputs in thecalculation. The high aerosol chloride
contents appear during the typhoon no. 2, 4, 6,7, 14 and 17 as shown in Fig.2. This leads us
to understand the main aerosol chlorides areproduced dramatically according to highswell and windy conditions. The amount of
SSA is dependent with the severe level ofeach typhoon including the direction ofwind-flux. This affirmation is strongly
recommended that the numbers of typhoons
should be mainly performed a function in themacro-scaled SSA estimation. The aerosol
chloride deposition on concrete surface isconsidered as the initial chloride ions flux.
The 1-year aerosol chlorides simulation isused to calculate the surface chloride content
and distribution in concrete of Ananai Bridge
at 37 years old. The simulation results areillustrated in Fig.3 which is compared withthe experimental data in Fig.4. The estimatedsurface chloride content is 9.2kg/m3 at 37years which comparatively precise with themaximum observed data at bottom-girderno.2 and front-girder no.3-5. In thesimulation of chloride ingression including
rain effect, the surface chloride dissolution istaken into account for raining days. The
raining duration (> 5mm/day) is totallycounted as 76 days in year 2003, same
proportion as 1-day wet to 5-days dry. The
simulated result is shown that the surface
chloride content is dropped to the level of
3.74 kg/m3. This result could be comparedwith the measured data from the front-side of
the first girder which subjects to rainfall ordrainage path. The simulation shows
overestimation of rain effect which might bethought as the effect of roof by top flange.
Conclusion
This life-span simulation indicated as time ofcorrosion initiation is proposed in asystematiccalculation
ofwavetransformation and breaking, SSA formation,transportation, and ingression into concrete.
Each mechanism doesn’t only depend on theconcrete strength and covering, but also theenvironmental characteristic of wind/wave,
landscape, temperature, pressure and etc.
Especially during typhoon attack; windy
condition, high swell, high temperatureseason and low in atmospheric pressure arecumulative circumstance to create large
amount of aerosol chloride and deposit on
structural surface. Total amount of aerosol
chloride deposition is equaled with theamount of chloride distributed along thecovering
depth.
In thisfree-spacetransportation model, an average aerosol
chlorides distribution at a certain distance canbe computed. The variation of surface
chloride contents of bridge members is due toaerosol chloride particles moving under
vortexshedding.
Unfortunately,
thisphenomenon is not well understood at thismoment, thus the further work on this subject
is truly necessary. Furthermore, the aerosol
chloride ingression into concrete is simply
expressed in Fick’s 2nd Law of diffusionconsidering the coupling of bound and freechlorides. Finally, a simple estimation ofchloride distribution in concrete at any ages
can be succeeded in order to indicate time ofcorrosion initiation as threshold limited
serviceability.

Fig.2. 1-year effective SSA content at Ananai bridge girder levelFig.3. Estimated surface chloride concentration and chloride distribution (kg/m3) at 37 years simulation

Fig.4. Structural monitoring on surface chloride contents of Ananai Bridge (kg/m3) after 37 years

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