### Ground water depths in Mobile County, AL

Ground water depths (GWD) in wells across Alabama are provided by the Geological Survey of Alabama (GSA)^{49}. We utilize this information to determine the GWD, measured with respect to ground level, at each of the 4,719 wells located in Mobile County (Supplementary Fig. S2.3a). The GWD measures were taken in different years; the oldest measure was in 1900, and the newest one was in 2017. The GWD from 1900 to 2000 has a mean measure of 48 m with a standard deviation (SD) of 30 m, while the mean decreased to 44 m and the SD increased to 34 m after 2000. Population growth and economic development in Mobile County are two reasons^{50} for the decrease in groundwater depth in recent years and, consequently, the increase in susceptibility of reinforced concrete foundations to SWI.

As shown in Supplementary Fig. S2.3a, the spatial distribution of the wells does not give good coverage of the area of interest. Thus, the wells can only provide GWD information for some of the buildings. Accordingly, the spatial distribution of the GWD over Mobile County was determined from the GWD data by a Kriging method^{51}. The accuracy of the interpolated GWD was measured by the Root Mean Square Error (RMSE), which was approximately 7 m and was considered relatively high for the purpose of this study. Dividing the area of interest into 8 regions, as shown in Supplementary Fig. S2.3a, reduced the RMSE error to roughly 3 m in each of the regions; however, that still was judged to be unacceptably high. Thus, we clustered the wells dataset inside each of the eight regions (Supplementary Fig. S2.3a) to calculate the cumulative distribution function (CDF) of GWD for the regions (Supplementary Fig. S2.3b). The CDF of the GWD in the 4719 wells was assumed to be lognormally distributed, using the following equation:

$$\text{P}\left(GWL \le {x}_{1}\right) =\Phi \left(\frac{(ln {x}_{1}) – \theta }{\omega }\right)$$

(1)

$${\omega }^{2}=\text{ln }(1 + \frac{\sigma }{\mu })$$

(2)

$$\theta =\text{ln }(\mu )- \frac{1}{2}{\omega }^{2}$$

(3)

where *Φ( )* = standard normal CDF, *x*_{1} is the state variable, \(\mu\) and \(\sigma\) are the mean and the standard deviation of the GWD in each region, and (*θ, ω*^{2}) = the logarithmic mean and logarithmic variance of the lognormal distribution.

Equation (1) is used to estimate the probability of a particular GWD value in the year 2020 for each region. For the GWD decrease, we assume that the saltwater under the freshwater level is closely linked to ocean fluctuations^{52}, as noted previously, and hence the GWD is assumed to be linearly related to SLR^{12,13}. In addition, based on the slow increase in sea level through the years and assuming the GWD in wells data has reached a stationary condition, the variations in water permeability (hydraulic conductivity usually ranges 1–50 cm/h^{53}) for different soil type (Supplementary Fig. S2.1) are not considered in this study. Supplementary Fig. S2.3c shows the anticipated SLR scenarios based on NOAA projections^{54} which has been used in previous studies^{6,8}. The ground water estimation is summarized in step 2(b) in Fig. 3.

### Estimated foundation depth (FD)

Two sources of data were used to identify soil types, as shown in Supplementary Fig. S2.1. The first is the Soil Survey Geographic Database (SSURGO)^{55}, which covers 75% of the area. The second is STATSGO, which gives generic (lower resolution) soil maps by state^{55}.

We used the following equation to determine the FD’s range based on the soil type at the site of each building^{56}:

$${D}_{min}= {\frac{q}{\gamma } \left[\frac{1 – sin \; {\upvarphi }}{1 + sin \; {\upvarphi }}\right]}^{2}$$

(4)

where D_{min} is the minimum depth of the foundation (the FD), \({\upvarphi }\) is the angle of repose (angle of friction), q is the bearing capacity of the soil, and \(\gamma\) is the density of the soil. Supplementary Table S2.1 gives more details for the values of each variable used in Eq. (4).

### Corrosion of steel in concrete foundations

Corrosion of reinforcement in concrete foundations is most often caused by external sources of chlorides, including deicing agents and saltwater, as well as concrete ingredients. When steel is embedded in concrete, it is naturally protected (passivated) against corrosion because of the high pH (alkaline) environment of the cement. Chloride ions penetrate the concrete cover through capillary absorption, hydrostatic pressure, and diffusion^{57}. Fick’s second law models the diffusion mechanism of chloride penetration^{22,58}.

$$C({x}_{2},t) = {C}_{0}\left[1-erf(\frac{{x}_{2}}{2\sqrt{Dt}})\right]$$

(5)

where erf ( ) is the error function, D is the diffusion coefficient, C_{0} is the surface chloride content, and C(x_{2},t) is the chloride content at a distance x_{2} in meters from the concrete surface at time t in years. Depassivation of the reinforcing steel occurs when chloride ions penetrate the concrete cover to the level of the reinforcement. Corrosion initiates when the chloride concentration at the reinforcing steel exceeds a threshold level, C_{th}. Supplementary Fig. S2.5 shows the probability of corrosion initiation (P(CI)) corresponding to each SWI scenario in Table 1 by modifying Eq. (5) to determine the corrosion initiation time t, when C(x_{2}, t) is replaced with C_{th}. The mean and standard deviation of corrosion initiation are predicted using Monte Carlo Simulation (MCS). Supplementary Table S2.2 gives more details of the random variables used in MCS and Eq. (5). The P(CI) is estimated as P(GWD ≤ x_{1}) \(\cap\) P(CI ≤ x_{2}) = P(CI ≤ x_{2}|GWD ≤ x_{1})*P(GWD ≤ x_{1}). Stewart et al.^{59} concluded that in the case of a high corrosion rate, the probability of corrosion damage is only slightly less than the probability of corrosion initiation. Thus, this study considers a corrosion rate due to the high chloride level assumed in SWI scenarios and the probability of corrosion initiation is regarded as the same as the probability of corrosion damage. Subsequent deterioration in strength is determined by loss of reinforcement area, cracking and spalling due to the expansive products of corrosion^{60}.

### Life cycle cost analysis

Life cycle costs associated with various corrosion damage mitigation strategies were calculated by using the following equation^{61}:

$$FR =PR{\left(1+i\right)}^{N}$$

(6)

where FR is the future repair cost, PR is the present repair cost, i is the periodic inflation rate, and N is number of years. In this study, we used PR equal to $15,000 if 5% ≤ P(CI) < 20% based on findings from the HomeAdvisor website for the maximum repair cost of buildings’ foundations^{62}. In addition, a foundation replacement of $75,000^{63} is assumed if corrosion has reduced the steel cross-section to less than 80% of its original diameter^{64}. Thus, we assumed to use PR equal to $75,000 if P(CI) ≥ 20%. For 1% ≤ P(CI) < 5% we assumed PR equal to $3000. The annual inflation rate was assumed to be 3%. The future repair cost is then multiplied by the probability of corrosion initiation to calculate the repair cost for each building at each year. Future costs of repairing, inspecting, and maintaining were computed using today’s pricing and approximated using Eq. (6) and a forecast inflation rate for comparisons of mitigation strategies. Then, using Eq. (7) and a discount rate, the present values of future costs were estimated.

$$DPR = \frac{FR}{{(1+d)}^{N}}$$

(7)

where DPR is the discounted present repair cost, d is the nominal periodic discount rate. According to the United States Office of Management and Budget (OMB)^{65}, the regulatory analysis real discount rate should be 7% or 3%, representing average private capital return in the US economy or the social rate of time preference, respectively. In this study we used the 6% discount rate to calculate the DPR value.

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