This paper presents simplified closed-form analytical solutions that can be used to interpret and predict ground movements caused by shallow tunneling in soft ground conditions These solutions offer a more comprehensive framework for understanding the distribution of ground movements than widely used empirical functions Analytical solutions for the displacement field within the ground mass are obtained for two basic modes of deformation corresponding to uniform convergence and ovalization at the wall of a circular tunnel cavity, based on the assumption of linear, elastic soil behavior Deformation fields based on the superposition of fundamental, singularity solutions are shown to differ only slightly from analyses that consider the physical dimensions of the tunnel cavity, except in the case of very shallow tunnels This work demonstrates a simplified method to account for soil plasticity in the analyses and illustrate closed-form solutions for a three-dimensional (3D) tunnel heading A companion paper describes applications of these analyses to interpret field measurements of ground response to tunneling

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Ground Movements due to Shallow Tunnels in Soft Ground. I: Analytical Solutions

Analytical expressions for the flow field as well as for the effective slip length of a shear flow over a surface with periodic rectangular grooves are derived. The primary fluid is in the Cassie state with the grooves being filled with a secondary immiscible fluid. The coupling of the two fluids is reflected in a locally varying slip distribution along the fluid–fluid interface, which models the effect of the secondary fluid on the outer flow. The obtained closed-form analytical expressions for the flow field and effective slip length of the primary fluid explicitly contain the influence of the viscosities of the two fluids as well as the magnitude of the local slip, which is a function of the surface geometry. They agree well with results from numerical computations of the full geometry. The analytical expressions allow an investigation of the influence of the viscous stresses inside the secondary fluid for arbitrary geometries of the rectangular grooves. For classic superhydrophobic surfaces, the deviations in the effective slip length compared to the case of inviscid gas flow are pointed out. Another important finding with respect to an accurate modelling of flow over microstructured surfaces is that not only the effective slip length, but also the local slip length of a grooved surface, is anisotropic.

Influence of the enclosed fluid on the flow over a microstructured surface in the Cassie state

Analytical formulas for gear body-induced tooth deflections of spur gears considering structure coupling effect

Strength degradation and stress analysis of composite plates with circular, square and rectangular notches using digital image correlation

Animals come in all shapes and size, from ants to elephants. In all cases, the tissues and organs in the animal’s body acquire their shape as the animal develops. Cells in developing tissues squeeze themselves or push and pull on one another, and the resulting forces generate the final shape. This process is called morphogenesis and it is often studied in a worm called Caenorhabditis elegans. This worm’s simplicity makes it easy to work with in the laboratory. Yet processes that occur in C. elegans also take place in other animals, including humans, and so the discoveries made using this worm can have far-reaching implications. As they develop, the embryos of C. elegans transform from a bean-shaped cluster of cells into the characteristic long shape of a worm, with the head at one end and the tail at the other. The force required to power this elongation is provided by the outer layer of cells of the embryo, known as the epidermis. In these cells, motor-like proteins called myosins pull against a mesh-like scaffold within the cell called the actin cytoskeleton; this pulling is thought to squeeze the embryo all around and cause it to grow longer. Six strips of cells, running from the head to the tail, make up the epidermis of a C. elegans embryo. Myosin is mostly active in two strips of cells that run along the two sides of the embryo. In the strips above and below these strips (in other words, those on the upper and lower sides of the worm), the myosins are much less active. However, it is not fully understood how this distribution of myosin causes worms to elongate only along the head-to-tail axis. Vuong-Brender et al. have now mapped the forces exerted in the cells of the worm’s epidermis. The experiments show that, in the strips of cells on the sides of the embryo, myosin’s activity causes the epidermis to constrict around the embryo, akin to a boa constrictor tightening around its prey. At the same time, the actin filaments in the other strips form rigid bundles oriented along the circumference that stiffen the cells in these strips. This prevents the constriction from causing the embryo to inflate at the top and bottom strips. As such, the only direction the embryo can expand is along the axis that runs from its head to its tail. Together, these findings suggest that a combination of oriented force and stiffness ensure that the embryo only elongates along the head-to-tail axis. The next step is to understand how this orientation and the coordination between cells are controlled at the molecular level.

The interplay of stiffness and force anisotropies drives embryo elongation.

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Some Basic Problems Of The Mathematical Theory Of Elasticity

This book comprehensively offers an interdisciplinary and dynamic account of the politicization of urban planning in Mumbai, India 

Leonie Moench

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Some Basic Problems Of The Mathematical Theory Of Elasticity

Politics of Urban Planning