Shallow foundation design: a comparative study of partial safety factors and full probabilistic methods.

In the past two decades, Europe has witnessed a significant transition in the design codes used for assessing foundation structures, with the widespread adoption of the Eurocodes (EC). This shift remains a pertinent topic within the engineering community, particularly concerning the transition from traditional design methodologies to those prescribed by the Eurocodes, as well as the potential for fully probabilistic design. While the Eurocodes' methodology is described as probabilistic, it is crucial to recognize that the achievement of the target reliability level is predominantly facilitated through a system of partial safety factors. These factors are integrated into the calculation algorithm as fixed values, rendering the process essentially deterministic. To refine these calculations for more accurate reliability estimates-expressed in terms of failure probability-a genuinely probabilistic framework is required, termed as fully probabilistic computation. This paper aims to elucidate the fully probabilistic calculation approach for the broader professional community, using the geotechnical application of shallow foundations as an illustrative example. We present a comparative analysis of this advanced approach with the standard foundation design according to EC7 and CSN 731001, the latter being a precursor in Europe for implementing the partial safety factor method. The discussion extends to a practical demonstration of full probabilistic design juxtaposed against the conventional partial safety factor method, using a shallow foundation case study. Furthermore, the paper delves into the impact of the tail behavior of uncertain or spatially varying soil parameters on the theoretical probability of failure, underscoring its significance in foundation design.

Spatiotemporal monitoring of hard tissue development reveals unknown features of tooth and bone development.

Mineralized tissues, such as bones or teeth, are essential structures of all vertebrates. They enable rapid movement, protection, and food processing, in addition to providing physiological functions. Although the development, regeneration, and pathogenesis of teeth and bones have been intensely studied, there is currently no tool to accurately follow the dynamics of growth and healing of these vital tissues in space and time. Here, we present the BEE-ST (Bones and tEEth Spatio-Temporal growth monitoring) approach, which allows precise quantification of development, regeneration, remodeling, and healing in any type of calcified tissue across different species. Using mouse teeth as model the turnover rate of continuously growing incisors was quantified, and role of hard/soft diet on molar root growth was shown. Furthermore, the dynamics of bones and teeth growth in lizards, frogs, birds, and zebrafish was uncovered. This approach represents an effective, highly reproducible, and versatile tool that opens up diverse possibilities in developmental biology, bone and tooth healing, tissue engineering, and disease modeling.

From computed tomography to finite element space: A unified bone material mapping strategy.

BACKGROUND: The spatially varying mechanical properties in finite element models of bone are most often derived from bone density data obtained via quantitative computed tomography. The key step is to accurately and efficiently map the density given in voxels to the finite element mesh. METHODS: The density projection is first formulated in least-squares terms and then discretized using a continuous and discontinuous variant of the finite element method. Both discretization variants are compared with the nodal and element approaches known from the literature. FINDINGS: In terms of accuracy in the L2 norm, energy distance and efficiency, the discontinuous zero-order variant appears to be the most advantageous. The proposed variant sufficiently preserves the spectrum of density at the edges, while keeping computational cost low. INTERPRETATION: The continuous finite element method is analogous to the nodal formulation in the literature, while the discontinuous finite element method is analogous to the element formulation. The two variants differ in terms of implementation, computational cost and ability to preserve the density spectrum. These differences cannot be described and measured by known indirect methods from the literature.

Bone mineral density modeling via random field: Normality, stationarity, sex and age dependence.

BACKGROUND AND OBJECTIVE: Capturing the population variability of bone properties is of paramount importance to biomedical engineering. The aim of the present paper is to describe variability and correlations in bone mineral density with a spatial random field inferred from routine computed tomography data. METHODS: Random fields were simulated by transforming pairwise uncorrelated Gaussian random variables into correlated variables through the spectral decomposition of an age-detrended correlation matrix. The validity of the random field model was demonstrated in the spatiotemporal analysis of bone mineral density. The similarity between the computed tomography samples and those generated via random fields was analyzed with the energy distance metric. RESULTS: The random field of bone mineral density was found to be approximately Gaussian/slightly left-skewed/strongly right-skewed at various locations. However, average bone density could be simulated well with the proposed Gaussian random field for which the energy distance, i.e., a measure that quantifies discrepancies between two distribution functions, is convergent with respect to the number of correlation eigenpairs. CONCLUSIONS: The proposed random field model allows the enhancement of computational biomechanical models with variability in bone mineral density, which could increase the usability of the model and provides a step forward in in-silico medicine.