Key Points Question Is the state expansion of Medicaid associated with rates of child physical abuse and neglect? Findings In this ecological study comparing pre– and post–Medicaid expansion state-level rates of child physical abuse and neglect from the National Child Abuse and Neglect Data Systems, after adjusting for confounders, there were fewer cases of reported neglect (422 fewer per 100 000 younger than 6 years) in states that expanded Medicaid than during that time in nonexpansion states, which had a baseline rate of 3944 cases per 100 000 children younger than 6 years in 2013. Meaning These results suggest that Medicaid expansion may serve as a means to prevent child neglect.

The heterogeneity of a cement-based material results in a random spatial distribution of carbonation depth. Currently, there is a lack of both experimental and numerical investigations aiming at a statistical understanding of this important phenomenon. This paper presents both experimental and numerical supercritical carbonation test results of cement mortar blocks. The carbonation depths are measured along the carbonation boundary by the proposed rapid image processing technique, which are then statistically studied by calculating, e.g., their probability density and power spectral density (PSD). The results indicate that the distribution of the carbonation depth can be approximately represented by a lognormal distribution function and the PSD has quantitative correlation with some of the statistic parameters used in the simulations. In particular, the effects of the autocorrelation lengths and the coefficient of variation of porosity, which are used to define the random porosity field, on the irregularity of carbonation depth are analyzed numerically in details and validated by experimental results. The study has shown that using a random field of porosity with due consideration of spatial correlation and variance, the irregularity of carbonation depth can be realistically captured by the numerical model. The numerical results confirm that lognormal distributions represent the random nature of carbonation depth well and the average and variance of the irregular carbonation depth increase with the increase of carbonation time, autocorrelation length and coefficient of variation of porosity. The study also offers a potential method to numerically calibrate some of the statistic parameters required by a numerical carbonation model through comparing the PSD with that from experimental tests. Overall the methodology adopted in the paper can provide a foundation for future investigations on probability analysis of carbonation depth and other similar work based on multi-scale and-physics modelling.

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Abstract:In this paper, the supercritical carbonation process of cement-based materials is modelled by introducing a random porosity field to simulate the heterogeneous geometry of the carbonation profile. The suitability of two different random fields of porosity, based on the Probability Density Function (PDF) and the Ellipsoidal Autocorrelation Function (EAF) methods, are investigated, respectively, in simulating the distribution of porosity in cement mortar. After incorporating the above random fields into an established supercritical carbonation model, it is found that with some modifications, the EAF method with consideration of spatial correlation produces better simulation of the irregularities of the carbonation zones that have been observed from experimental results. It is also found that for given average porosity and coefficient of variation, the predicted average and maximum carbonation depths have much smaller coefficients of variation. The validated EAF supercritical carbonation model is then used in parametric studies that are conducted to assess the effect of various factors on the carbonation depth of the chemical process.