Abstract
Silane is one of the favorable surface treatment materials in practical engineering due to its superiority in rendering the treated concrete with breathability,durability and aesthetics[1].In contrast to its wide application,the service life extension effect of silane is not suf ficiently considered in most design codes,and the treatment is usually regarded as an additional protective measure,leading to an uneconomic design of cover thickness.
To bridge this gap,the durability design of silane treated concrete structures is carried out in a model-based way.The bilayer physical model proposed by Zhang et al.[2]is used herein to predict the chloride transport process,in which the hydrophobic layer formed after silane impregnation is distinguished from the substrate concrete(Figure 1).
The diffusivity of substrate concrete can be described by the Life-365 model[3],and the coef ficient of the treated area is further gained by multiplying an exponential discount function[4].The water repellent layer thickness can be calculated after incorporating influential factors with the model proposed by Johnasson et al.[5],and the thinning effect of the hydrophobic layer is also considered with an exponential model gained from the regression analysis.The model was built and solved with the COMSOL multiphysics.
Figure 1 Chloride transport in treated concrete
The inevitable uncertainty of the deterioration process was considered through Monte Carlo simulation,and Latin Hypercube sampling technique was applied in advance to control the computational workload of solving numerical models.A total number of 1 000 samples were generated according to the distributions of model parameters(Table 1).
Table 1 Statis tical properties of parameters
The model was verified with on-site exposure data gained from Scotland[6],Belgium[7]and Iran[8],and used to conduct durability design.
The design can be conducted in a fully probabilistic way,and the sensitivity analysis reveals that the service life of silane treated structures can be greatly influenced by the cover thickness and water-cement ratio,which is similar to the untreated structures(Figure 2).
Figure 2 Sensitivity analysis of corrosion-free life
A more practical partial factor method is then proposed for the convenience of engineering practice,and the protection of silane is converted into an additional layer of concrete cover(xe)in the design equation.
Further analysis shows that xe can be influenced by water-cement ratio,surface moisture content and the original cover thickness,but varies little with the temperature and the target reliability index.The exact values for concrete with a watercement ratio of 0.4 are listed in Table 2.
By choosing the mean values as the characteristic values of random variables,the partial factors can be determined following the first order reliability theory(FROM)[9],and the durability design can be conducted with Eq.(1).The partial factors determined are shown in Table 3.
Table 2 xe in various conditions(β=1.0,1.3,1.5)
Table 3 Partial factors determined with FORM
A representative case(Splash zone,T=15℃,RH=0.7,W/C=0.4,βt=1.0,tSL=70a)was chosen to illustrate the process and verify the effectiveness of the proposed method.Through comparisons with the thickness designed by fully probabilistic method,it is clear that the result(xd,s=69mm)is sufficiently safe and ensures achieve a reliability level of more than 1.20.It is believed that the conservative design is mainly attributed to the consideration of concrete cover thickness tolerance(Δx),which is necessary considering the uncertainty in the construction stage.