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Knowledge of the in situ stress state of rock mass is fundamental for engineering, geological and geophysical applications. In situ stress state determination requires in principle the evaluation of the three principal stresses and the related principal directions, but it is widely recognized in the literature that the maximum horizontal stress is the most difficult component to accurately estimate. In the context of borehole methods, this paper proposes a step-by-step analytical procedure to estimate some bounds to the maximum horizontal stress, starting from a geomechanical description of the rock and relying on information generally available in the engineering practice. The procedure is divided in substeps, each one requiring additional information about the mechanical properties of the rock and on the geometrical properties of the failed portion of rock: more information available implies a lower uncertainty on in situ stress estimate. Furthermore, since the proposed procedure is analytical, it allows a complete and very easy implementation in a spreadsheet. The aim of the work is thus to provide a rigourous but simple analytical tool that can be used in engineering practicte to estimate some bounds to the maximum horizontal in situ stress state. The approach is finally validated by means of both numerical simulations, performed with a sophisticated numerical tool, and experimental field data coming from the literature.

We present a method for constructing blades of hydroelectric turbines and ship propellers based on design parameters that possess a clear hydraulic meaning. The design process corresponds to the classical construction of a blade using the medial surface of the blade and profile curves attached to it. The main new contribution of the paper consists in realizing this construction using B-spline techniques. In particular, it is shown how to obtain blade boundary surfaces (which describe the pressure and the suction side of the blade) which are joined with C^1-smoothness along the leading edge. Moreover, special attention is paid to the construction of propeller blades with a well-defined tangent plane at the tip, which is a singular point of the blade boundary surfaces. In order to guarantee these smoothness properties, we generate and analyze singularly parameterized medial surfaces. We contribute novel shape modeling techniques that are based on singular parameterizations and demonstrate their potential for applications in industry. Finally, it is shown how to represent the blades as B-spline surfaces with a relatively small number of control points.

We present a simplified model of damaging porous material, obtained through consistent linearization from a recursive-faulting material model described in (Pandolfi et al. 2016). The brittle damage material model is characterized by special planar micro-structures, consisting of nested families of equi-spaced frictional-cohesive faults in an otherwise elastic matrix material. The linear kinematics model preserves the main microstructural features of the finite kinematics one but offers a far better computational performance. Unlike models commonly employed in geo-mechanical applications, the proposed model contains a small number of parameters, to wit, two elastic moduli, three frictional-cohesive parameters, and three hydraulic response parameters, all of which having clear physical meanings and amenable to direct experimental measurement through standard material tests. The model is validated by comparison to triaxial hydro-mechanical experimental data. Despite the paucity of material constants, the salient aspects of the observed behavior are well captured by the model, qualitatively and quantitatively. As an example of application of the model, we simulate the excavation of a borehole in a rocky embankment.