Investigation of the Effect of Bedding Layer Angle and Tunnel Number on the Stability of Tunnel under Uniaxial Compression Using PFC2D

In this paper the effect of bedding layer angle on the stability of tunnel under uniaxial compression have been investigated using particle flow code in two dimensions (PFC2D). For this purpose, numerical rectangle models with dimension of 100*100 mm have been prepared. These models consist of layers with different mechanical properties i.e., concrete layer and gypsum layer. The angle of these layers related to horizontal axis change from 0° to 90° with increment of 15°. These models are consisting of one, two and three tunnel. The diameter of tunnel change based on the tunnel number. The tunnel diameter was 6 m, when one tunnel exists in the model. The tunnel diameter was 3 m, when two tunnels exist in the model. The tunnel diameter was 2 m, when three tunnels exist in the model. These models were subjected to uniaxial compression. The results show that tensile cracks are dominant mode of fracture occurred in the models. The joint angle and tunnel number have important effect on the failure pattern and failure strength. Also, the mechanical properties of beddings control the crack growth path. The crack grows through the weak layers when bedding angle was equal to 45° and 60°, but it intersects the layer for any other bedding angels.

Engineering geological characteristics based on rock mass rating (RMR) and geological strength index (GSI) in Tunnel Number 1 of the Sigli-Aceh toll road

This paper presents engineering geological investigation results in the form of rock mass characteristics for tunnel number 1 of the Sigli-Aceh toll road. The investigation was carried out through geological mapping, core drill evaluation, and laboratory tests. In this research, the rock mass rating (RMR) and Geological Strength Index (GSI) were applied for the rock mass classifications. The measurement of rock mass quality is then used to determine the excavation method and tunnel support system on the SigliAceh toll road. The results showed that the research location consisted of calcareous sandstone with poor to good-quality (GSI (21.7 - 85.5), RMR (32.0 - 67.6)), and sandstone with good quality (GSI (86.3 - 86.9), RMR (64.0 - 65.0)). The poor quality rock masses were mainly caused by weathering effect. In addition, this research also analyzes the relationship between RMR and GSI based on the type and quality of rocks in the research location so that this correlation can be used in other areas with similar rock type and quality to this research location.

Hyperbolic tunnel-number-one knots with Seifert-fibered Dehn surgeries

Suppose [Formula: see text] and [Formula: see text] are disjoint simple closed curves in the boundary of a genus two handlebody [Formula: see text] such that [Formula: see text] (i.e. a 2-handle addition along [Formula: see text]) embeds in [Formula: see text] as the exterior of a hyperbolic knot [Formula: see text] (thus, [Formula: see text] is a tunnel-number-one knot), and [Formula: see text] is Seifert in [Formula: see text] (i.e. a 2-handle addition [Formula: see text] is a Seifert-fibered space) and not the meridian of [Formula: see text]. Then for a slope [Formula: see text] of [Formula: see text] represented by [Formula: see text], [Formula: see text]-Dehn surgery [Formula: see text] is a Seifert-fibered space. Such a construction of Seifert-fibered Dehn surgeries generalizes that of Seifert-fibered Dehn surgeries arising from primtive/Seifert positions of a knot, which was introduced in [J. Dean, Small Seifert-fibered Dehn surgery on hyperbolic knots, Algebr. Geom. Topol. 3 (2003) 435–472.]. In this paper, we show that there exists a meridional curve [Formula: see text] of [Formula: see text] (or [Formula: see text]) in [Formula: see text] such that [Formula: see text] intersects [Formula: see text] transversely in exactly one point. It follows that such a construction of a Seifert-fibered Dehn surgery [Formula: see text] can arise from a primitive/Seifert position of [Formula: see text] with [Formula: see text] its surface-slope. This result supports partially the two conjectures: (1) any Seifert-fibered surgery on a hyperbolic knot in [Formula: see text] is integral, and (2) any Seifert-fibered surgery on a hyperbolic tunnel-number-one knot arises from a primitive/Seifert position whose surface slope corresponds to the surgery slope.

On links minimizing the tunnel number

We determine a large class of links, including some satellite and hyperbolic links, for each of which the tunnel number is the minimum possible, the number of its components minus one, and observe that the rank versus genus conjecture is valid for this class of links.

Thurston norms of tunnel number-one manifolds

The Thurston norm of a three-manifold measures the complexity of surfaces representing two-dimensional homology classes. We study the possible unit balls of Thurston norms of three-manifolds [Formula: see text] with [Formula: see text], and whose fundamental groups admit presentations with two generators and one relator. We show that even among this special class, there are three-manifolds such that the unit ball of the Thurston norm has arbitrarily many faces.

2-Component links with genus two Heegaard splittings

In the present paper, we consider two types of 2-component links with genus two Heegaard splittings. One of them is an ordinary tunnel number one link, and the other is a somewhat different tunnel number one link. We will try to detect the differences between those two types. In fact, we will characterize composite tunnel number one links of the second type, and tunnel number one links of the second type with essential tori.