Soil structure quality can be scored by visual examinations or measured with soil physical properties. To investigate the relationships between these two approaches, we adapted the VESS (Visual Evaluation of Soil Structure, Guimarães et al., 2011) to the scoring of cores (CoreVESS) on which shrinkage analysis was also performed. Scoring was performed blindly after equilibrating the samples at −100 hPa matric potential and was compared to soil texture, soil organic carbon content (SOC), soil hydrostructural stability, structural porosity, plasma porosity, bulk soil porosity or density, and water content at standard matric potential. A large geographical area of Cambi-Luvisols was sampled at 55 locations with different soil management in western Switzerland. VESS was performed on the pits and layers prior to sampling undisturbed cores. Sandy soils presented medium CoreVESS scores compared to clayey soils. Only soils with more than 20% clay content obtained good scores in this study. The relationships between CoreVESS scores, SOC and most physical properties followed a broken-stick regression, with most breaking points close to score 3. Most regressions were significant and highly determined with R2 above 0.45. Linear decrease with CoreVESS scores was observed for total porosity and bulk density of air-dried soil and for water content at −10hPa. The underlying model of structural quality decrease can be summarized as follows. From score 1 to 3 the decrease in structure quality corresponds to a decrease in SOC. From score 1 to 2 occurs most of the decrease in coarse porosity volume. From score 3 to 5 the decrease of structure quality corresponds to a loss of structural porosity, which converges to 0 cm−3 g−1 for score 5, and to a collapse of the samples upon drying between scores 3 and 4, thus denoting a loss of hydrostructural stability. VESS scores of pits and layers were poorly correlated to CoreVESS scores and physical properties, probably due to local variability of the sampled layers. Our results suggest that the relation between visual scoring and physical properties is not site specific, and underline the need for standardizing the moisture conditions in soil structure quality assessment.