Proceedings of the International rilem conference Materials, Systems and Structures in Civil Engineering 2016

71

International RILEM Conference on Materials, Systems and Structures in Civil Engineering 

Conference segment on Service Life of Cement-Based Materials and Structures 

22-24 August 2016, Technical University of Denmark, Lyngby, Denmark 

 

by CO

2

 in atmosphere, the chloride-induced corrosion of reinforcement steel by the chloride 

in sea water, the physical and chemical attack of salts (SO

4

2-

, Mg

2+

) in sea water and soils. 

Moreover, the alkali-aggregate reaction and the delayed-ettringite formation (DEF) should be 

avoided given the crucial function of concrete elements. The global philosophy of durability 

design with respect to these deterioration processes is to formulate the requirements on both 

material and structural levels, combining the material design with the structural design to 

achieve a working life of 120 years. For the raw materials of structural concretes, the mass 

ratio of calcium aluminates (C

3

A) in cement is controlled to 5%-8%; the SO

3

 content is 

controlled to below 4% of binder; the aggregates are required to be not alkali-reactive and the 

alkali content of concrete is controlled to 3kg/m

3

. By these specifications, the risks of salt 

attacks and internal expansion reactions are regarded low enough to be acceptable. 

Accordingly, the carbonation-induced corrosion and chloride-induced corrosion remain as the 

most critical processes for durability design. 

 

The design working life of whole project is 120 years. Aiming at this target, the durability 

design at structural level should firstly determine the working lives for structural elements on 

the basis of their structural importance and technical feasibility. The principal elements adopt 

the same working life as whole project, 120 years, and the secondary or replaceable elements 

can adopt shorter lives. For these elements, the maintenance and replacement schemes should 

be specified in design phase. Durability limits states (DLS) are needed for quantitative 

durability design [2]. These states are specified as the minimum acceptable performance 

levels for different durability processes [3]. For carbonation-induced and chloride-induced 

corrosion processes, two DLS can be defined: (a) corrosion initiation; (b) corrosion to an 

acceptable extent. In the project, PC elements, principal RC elements and RC elements with 

high maintenance difficulty should adopt DLS (a) while secondary RC elements can adopt 

DLS (b). 

 

2.2  Model-based design for chloride ingress 

The design model for chloride induced corrosion is adapted from the widely used analytical 

model of Fick’s second law [4,5]. With the DLS specified as the corrosion initiation, i.e. DLS 

(a), the design equation in partial factor format writes, 

 

cr

1

0

Cl

G

1 erf

0

2

nom

d

d

s

s

c

D

SL

C

x

x

C

D

t

   

(1) 

 

Here, C

cr,s

 stand for the threshold chloride concentration for steel corrosion and the concrete 

surface chloride concentration (%binder) respectively; x

d

nom

 and  x

d

 are the concrete cover 

nominal thickness and its construction error (m); D

Cl

0

 is the chloride diffusivity of concrete at 

a given age (m

2

/s);   is the ageing factor of concrete chloride diffusivity (-); t

SL

 is the design 

service life of structural elements; erf is the mathematical error function. The terms, 

c,s,D

, 

are the partial factors for the corresponding parameters. The ageing factor   describes the 

gradual decrease of concrete chloride diffusivity with time, 

 

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72

International RILEM Conference on Materials, Systems and Structures in Civil Engineering 

Conference segment on Service Life of Cement-Based Materials and Structures 

22-24 August 2016, Technical University of Denmark, Lyngby, Denmark 

 

0

Cl

0

0

Cl

,

n

t

D

t

t t

D

t

  with  

0

0

,

30 years

,

30 years

t t

t t

 (2) 

 

Here, the term n is the exponential coefficient for the ageing law and D

Cl

0

 the concrete 

diffusivity at age t

0

. Since it is not rational to assume this densification is to develop 

infinitively, this decrease law is truncated at t = 30 years to ensure the conservative design.  

 

To apply this design model, the characteristic values for the parameters and their 

corresponding partial factors should be determined for the concrete structures in HZM 

project. To this purpose, the statistical properties are regressed for the design parameters, C

cr

, 

C

s

, x

d

, D

Cl

0

 and n, from the long-term exposure tests on a similar exposure site (Zhanjiang 

Exposure Station) and structural inspections during the recent 30 years. The detailed 

statistical properties and the regression details were reported in [6,7]. On the basis of the 

obtained statistical properties, the partial factors and characteristic values for design 

parameters are calibrated through a fully probabilistic scheme for a target reliability index of 

=1.3 [7]. 

 

 

2.3  Model-based design for carbonation 

The carbonation model is an extended form of the widely used square time law for 

carbonation depth x

c

 [4,5], and the design equation is expressed in partial factor format as, 

 

-1

2

SL

ACC,0 R

CO2

SL

RH

G

2

0

d

c

d

t

e

c

t

t

h

x

x t

x

W

k

k k R

C

t

 (3) 

Here,  W

t

 is the weather function expressing the influence of atmospheric precipitation on 

concrete carbonation process (-); k

e

 is the environmental factor of humidity with detailed 

expression in (fib 2006) (-); k

c

 is the curing factor defining the influence of curing time during 

concrete hardening (-); (k

t

R

ACC

,

0

-1

+

t

) is the carbonation resistance of concrete in natural 

environment;  R

ACC,0

-1

 is the concrete carbonation resistance in accelerated test conditions 

(20ºC, RH=65%), in (mm

2

/year)/(kg/m

3

);  k

t

 is the regression parameter between the two 

resistances; 

t

 is the error term; C

CO2

 is the CO

2

 concentration in atmosphere (kg/m

3

) and t

SL

 

is the design life (year). The terms 

RH,R

 are partial factors for relative humidity and concrete 

carbonation resistance. The equation (3) takes the corrosion initiation as DLS. 

 

The design value of cover thickness x

d

 refers to x

d

nom

- x

d

. The statistical properties for the 

parameters needed for partial factor calibration can be found in [5]. Four representative cases 

are considered: interior surface and exterior surface of concrete elements for service lives of 

50 years and 120 years. Compared to interior surface, exterior surfaces have elevated 

humidity and lower weather function due to rain exposure conditions. For CO

2

 concentration, 

a high concentration of 32.8×10

-4

, four times of design value, is also retained to consider the 

possible CO

2

 accumulation in the tunnel by automobile exhaust. The characteristic values of 

concrete cover thickness x

d

nom

 and the carbonation resistance R

ACC,0

-1

 are retained as design 

parameters. 

 

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