Effect of Geometric Parameters and Construction Sequence on Ground Settlement of Offset Arrangement Twin Tunnels

A parametric study that examines the ground surface settlement due to the excavation of shallow offset arrangement twin tunnels is presented. Offset arrangement tunnels are those that run parallel to each other, but at different elevations. The study focuses on the influence of both the construction sequence and various geometric parameters on the induced soil settlement. A series of three-dimensional finite element analyses was carried out to investigate the settlement behavior and interactions between offset arrangement twin tunnels excavated in clay using a simplified mechanized excavation method. Analyses were carried out for three cover-to-diameter (C/D) ratios, three possible construction sequences, five angular relative positions, and five angular spacings. In addition, settlement data were also investigated by varying horizontal and vertical spacings while keeping the angular spacing constant. The total settlement of the excavated twin tunnels and the settlement induced solely by the new second tunnel are both presented, and special attention was paid to identifying the dominant geometric parameters. The observed data trends from this study are generally consistent with the limited data available in the literature. This study confirmed a few perceived behaviors. First, angular relative position better describes the settlement behavior in comparison to angular spacing. Second, the effect of the vertical distance is noticeably more significant than that of the horizontal distance between the two tunnels. Third, excavation of the lower tunnel at first induces higher total ground settlement than when the upper tunnel is excavated first or when both tunnels are excavated concurrently. Fourth, settlement due to the construction of the newer tunnel decreases with the increase in the cover depth. In addition, two design charts have been proposed to calculate the settlement induced from a new second tunnel excavation and the eccentricity of the maximum total settlement relative to the center of the new tunnel.

Dimensional Synthesis of a Novel 3-URU Translational Manipulator Implemented through a Novel Method

A dimensional synthesis of parallel manipulators (PMs) consists of determining the values of the geometric parameters that affect the platform motion so that a useful workspace with assigned sizes can be suitably located in a free-from-singularity region of its operational space. The main goal of this preliminary dimensioning is to keep the PM far enough from singularities to avoid high internal loads in the links and guarantee a good positioning precision (i.e., for getting good kinematic performances). This paper presents a novel method for the dimensional synthesis of translational PMs (TPMs) and applies it to a TPM previously proposed by the author. The proposed method, which is based on Jacobians’ properties, exploits the fact that TPM parallel Jacobians are block diagonal matrices to overcome typical drawbacks of indices based on Jacobian properties. The proposed method can be also applied to all the lower-mobility PMs with block diagonal Jacobians that separate platform rotations from platform translations (e.g., parallel wrists).

Construction of conical axoids on the basis of congruent spherical ellipses

Purpose: To carry out the transition from a cylindrical gear in which the centroids are congruent ellipses with centres of rotation in the foci, to a bevel gear on the basic of congruent spherical ellipses. Design/methodology/approach: Congruent ellipses with centres of rotation in the foci serve as centroids for the design of cylindrical gears with non-circular wheels. The article analytically shows that the analogues of ellipses on the plane - congruent spherical ellipses are the basis for the construction of the axoids of the corresponding bevel gears. An analogue of the centre-to-centre distance for ellipses in the plane is the angle between the axes of rotation of conical axoids. Findings: Based on the equality of the arcs of ellipses, the dependence of the angle of rotation of one axoid on the angle of rotation of another is found. Graphs of this dependence for separate cases are given. It is shown under what conditions the axes of axoids intersect at right angle. The parametric equations of spherical ellipses and corresponding axoids are given. They were used to construct spherical ellipses and corresponding conical axoids for different cases. For gears with right angle between the axes, separate positions of the axoids with different angles of their rotation around their axes are constructed. Practical implications: Spherical ellipses are directing curves for the construction of the corresponding conical axoids. Originality/value: The paper shows that congruent spherical ellipses act as centroids for the design of axoids of bevel gears. They roll one by one without sliding, rotating around axes that intersect in the centre of the sphere. To design such gears, it is important to know the interdependence between the geometric parameters, especially for common gears with a right angle between the axes.