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Abstract Experimental evidence shows that the strength of granular soils is significantly influenced by inherent cross anisotropy which cannot be properly described by isotropic failure criteria. This paper reviewed laboratory test results of various sands at different fabric directions. Based on the observations, this paper formulates the hypothesis that deposit plane creates a plane of weakness and the anisotropic strength of sands depends on orientations of deposit plane and failure plane. The strength decreases when orientations of deposit plane and failure plane are close to each other, and the strength increase when they diverge from each other. Then, an anisotropic failure criterion is developed based on this hypothesis and validated by available experimental data from literature. Remarkable agreements between predictions and measurements have been observed, which demonstrate validity, effectiveness, and robustness of new criterion in characterizing anisotropic strength of sands with variations of loading directions and intermediate principal stresses. 

Soil particles that have been deposited through water or air generally align their largest projected surface area normal to the depositional direction, which generates a cross-anisotropic fabric of granular soils. Researchers have used both two-dimensional (2D) and three-dimensional (3D) images to determine scalar fabric parameters of granular soils, including void ratio, coordination number, and average branch vector length. This study aims to evaluate the accuracy and effectiveness of 2D images to characterize fabric in 3D soils based on scalar parameters. The X-ray computed tomography (X-ray CT) is used to reconstruct the 3D volumetric images of three air-pluviated sand specimens, including crushed limestone, Griffin sand, and glass beads. Then, six slices are obtained by vertically cutting the 3D volumetric image in an angle increment of 30 degrees. The 3D and 2D images are analyzed to determine scalar fabric parameters. The results show that coordination numbers and average branch vector lengths computed from 2D images underestimate these values in 3D granular soils. The void ratios computed from 2D images vary a large range depending on slicing directions, which cannot provide reliable fabric characterizations for 3D granular soils. 

INTRODUCTION Thousands of genetic variants have been associated with human diseases and traits through genome-wide association studies (GWASs). Translating these discoveries into improved therapeutics requires discerning which variants among hundreds of candidates are causally related to disease risk. To date, only a handful of causal variants have been confirmed. Here, we leverage 100 million years of mammalian evolution to address this major challenge. RATIONALE We compared genomes from hundreds of mammals and identified bases with unusually few variants (evolutionarily constrained). Constraint is a measure of functional importance that is agnostic to cell type or developmental stage. It can be applied to investigate any heritable disease or trait and is complementary to resources using cell type– and time point–specific functional assays like Encyclopedia of DNA Elements (ENCODE) and Genotype-Tissue Expression (GTEx). RESULTS Using constraint calculated across placental mammals, 3.3% of bases in the human genome are significantly constrained, including 57.6% of coding bases. Most constrained bases (80.7%) are noncoding. Common variants (allele frequency ≥ 5%) and low-frequency variants (0.5% ≤ allele frequency < 5%) are depleted for constrained bases (1.85 versus 3.26% expected by chance, P < 2.2 × 10 −308 ). Pathogenic ClinVar variants are more constrained than benign variants ( P < 2.2 × 10 −16 ). The most constrained common variants are more enriched for disease single-nucleotide polymorphism (SNP)–heritability in 63 independent GWASs. The enrichment of SNP-heritability in constrained regions is greater (7.8-fold) than previously reported in mammals and is even higher in primates (11.1-fold). It exceeds the enrichment of SNP-heritability in nonsynonymous coding variants (7.2-fold) and fine-mapped expression quantitative trait loci (eQTL)–SNPs (4.8-fold). The enrichment peaks near constrained bases, with a log-linear decrease of SNP-heritability enrichment as a function of the distance to a constrained base. Zoonomia constraint scores improve functionally informed fine-mapping. Variants at sites constrained in mammals and primates have greater posterior inclusion probabilities and higher per-SNP contributions. In addition, using both constraint and functional annotations improves polygenic risk score accuracy across a range of traits. Finally, incorporating constraint information into the analysis of noncoding somatic variants in medulloblastomas identifies new candidate driver genes. CONCLUSION Genome-wide measures of evolutionary constraint can help discern which variants are functionally important. This information may accelerate the translation of genomic discoveries into the biological, clinical, and therapeutic knowledge that is required to understand and treat human disease. Using evolutionary constraint in genomic studies of human diseases. ( A ) Constraint was calculated across 240 mammal species, including 43 primates (teal line). ( B ) Pathogenic ClinVar variants ( N = 73,885) are more constrained across mammals than benign variants ( N = 231,642; P < 2.2 × 10 −16 ). ( C ) More-constrained bases are more enriched for trait-associated variants (63 GWASs). ( D ) Enrichment of heritability is higher in constrained regions than in functional annotations (left), even in a joint model with 106 annotations (right). ( E ) Fine-mapping (PolyFun) using a model that includes constraint scores identifies an experimentally validated association at rs1421085. Error bars represent 95% confidence intervals. BMI, body mass index; LF, low frequency; PIP, posterior inclusion probability.