Figure 1 shows a schematic of the glue-spall mechanism, and the corresponding stresses. The stress at the perimeter of the epoxy islands is known as the glue spall stress, σgs; This stress is responsible for the edge cracking in the substrate. In chapter 3 (Request this document) of my Ph. D. thesis it is shown that σgs ~ 2.5 MPa for the ice/cement system, which is very close to the tensile strength of cementitious media (3 MPa). However, salt scaling necessitates the propagation of cracks through the surface layer, so it is the toughness of the surface that governs the susceptibility to damage. It is reasonable to suggest that the surface is weakened by exposure and traffic. Therefore, much like the epoxy/glass system we expect that scaling will occur by propagation of preexisting flaws.

Figure 1 - (A-C) Schematic representation of the glue-spall mechanism. A) sandblasted glass surface, B) Epoxy/Glass composite at initial temperature, T0, and C) Interface of composite, illustrating the islands of epoxy and the thin scallops of glass removed when T << T0. (D-E) Schematic representation of an epoxy/glass/epoxy sandwich seal and the stress that arises in the composite. D) Sandwich seal, dimensions and orientation. E) Schematic of stress that arises in the glass surface under the epoxy, σg, in the epoxy, σe, and the glue-spall stress around the boundary of the epoxy, σgs.

Figure 2 - Results from classic scaling study by Verbeck and Klieger showing the amount of scaling damage versus the solute concentration. The scale rating is a subjective quantification of the amount of scaling that occurs where, 0=no scaling, and 5=severe scaling. In most cases severe scaling corresponds to a material loss of > 1 kg/m2. On the plot it is indicated how the mechanical response of ice accounts for the pessimum concentration.

Therefore, the ice layer must fail for scaling to occur. A trivial calculation, indicates that the residual stress in pure ice will rise above the strength of the ice after only 4°C of undercooling; So pure ice is expected to cause scaling damage. This implication is not consistent with a pessimum concentration (Figure 2). The characteristics of the pessimum are:

  • 1) little damage with pure water
  • 2) a maximum in damage at a moderate solute concentration
  • 3) little damage at higher solution concentrations

This discrepancy is due to the fact that ice exhibits rapid viscoelastic stress relaxation. It has been shown that the creep rate in ice is proportional to σ3. With this information we performed a viscoelastic stress calculation that consisted of calculating the stress in an ice layer on a concrete slab (so tf<< tc) when the temperature is reduced from 0 to -20°C in a period of 3 hr. The volume fraction of ice formed from a salt solution was calculated from the lever rule, and the creep rate in the ice layer was based on the volume averaged stress in the ice. The results indicated that the VE stress relaxation keeps the stress in a pure ice layer below the strength, while that in brine ice formed from a 2-4% NaCl solution rises above the strength, and more highly concentrated solutions do not gain strength in the temperature range of interest. The stress was also calculated for various cooling rates, and it was determined that the rate had little effect on the results. The limited dependence on cooloing rate is a result of the strong relationship between the creep strain rate and stress. Thus, as Figure 2 indicates the effect of brine pockets on the mechanical properties of ice account for the pessimum concentration.

Figure 3 - Results from a viscoelastic stress calculation of the stress in an ice layer on a sidewalk. The results show that the stress in pure ice remains below the strength, while the opposite is true for ice formed from a 3% NaCl solution. In the plots, Φ is the volume fraction of ice, and σ stands for stress/strength, as indicated.