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Measuring stiffness of soils in situ
Published in Fusao Oka, Akira Murakami, Ryosuke Uzuoka, Sayuri Kimoto, Computer Methods and Recent Advances in Geomechanics, 2014
Fusao Oka, Akira Murakami, Ryosuke Uzuoka, Sayuri Kimoto
The elastoplastic and viscoplastic subloading surface models presented by (Hashiguchi 2009) assumed that the yield surface is a homogeneous function of degree one. In the present work, this restriction is removed. Instead, the yield surface is formulated taking into account the geometric concept of homothety, i.e., the yield and subloading surfaces are uniformly scaled between them relative to the centre of homothety. This implies the definition of a homothety ratio or scaling factor.
Illogical use of the converse of a theorem that can cause an incorrect solution
Published in International Journal of Mathematical Education in Science and Technology, 2022
Then the teacher suggested considering the case of an obtuse angle ∠C. In this case the midline DE of triangle ABC is the only segment of length t if DC ≤ t. But the students found it difficult to imagine what the set S of points A would look like for this case. Therefore the teacher suggested finding the locus of the points A for which DC = t using DGE software (GeoGebra). For this purpose a suitable applet was prepared (https://www.geogebra.org/m/rwtcwpyb). The applet allows with the help of a special slider to move the point D around the circle of radius t and with the center at point C, and observe the trajectory of the movement of point A so that the point D remains the middle point of the segment AB. Using the applet the students discovered that the trajectory of point A is also a circle. Then they were asked to explain this fact. Since the students had already studied the course of Euclidean geometry, 30 of them (83%) correctly noticed that the trajectory of point A can be obtained from the trajectory of point D using a homothety of ratio 2 with the center at point B because for each position of points A and D, they are on the ray BD and satisfy BA: BD = 2 (Figure 10). Accordingly, the center of the obtained circle O is on the ray BC so that BO=2BC.
Rheological properties, 2S2P1D modelling and SHStS transformation of 12 Brazilian bitumens and mixtures
Published in Road Materials and Pavement Design, 2021
Évelyn Paniz Possebon, Luciano Pivoto Specht, Hervé Di Benedetto, Silvio Lisboa Schuster, Deividi da Silva Pereira
On a Cole–Cole plan, Equation (3) relationship correspond to the sequence of a shift along the horizontal axis, a homothetic transformation, a shift of characteristic time and a second shift along the horizontal axis (Figure 4). That is why, this transformation is called Shift-Homothety-Shift and time-Shift (SHStS) (Pouget et al., 2010, 2012; Tiouajni et al., 2011). When plotted in a Cole–Cole diagram, normalized modulus of materials (mixtures, mastics, etc.) produced with the same bitumen generate curves that overlaps. It proves that the TTSP is originated from the bitumen behaviour, regardless of the aggregate skeleton. It is possible to predict the LVE behaviour of the bituminous mixtures from the LVE properties of the corresponding bitumen and vice versa.
Review of experimental characterisation and modelling of asphalt binders at low temperature
Published in International Journal of Pavement Engineering, 2018
Mihai O. Marasteanu, Augusto Cannone Falchetto
An interesting application of the Huet model is associated with the possibility of obtaining an expression relating the low-temperature properties of asphalt binder and asphalt mixture through a simple formulation named Shift-Homothety-Shift in time-Shift (SHStS) transformation. This transformation, originally known as ENTPE (École Nationale des Travaux Publics de l’État) transformation, was initially proposed by Di Benedetto and his research group in the frequency domain (Di Benedetto et al. 2004, Pouget et al.2010). A formulation of the SHStS transformation in the time domain was derived by Cannone Falchetto et al. in (2011). This expression is based on the simple linear relationship between the characteristic time, τ, of binder and corresponding mixture.