Estimation of the Critical Seismic Acceleration for Three-Dimensional Rock Slopes

An analytical approach for the estimating of critical seismic acceleration of rock slopes was proposed in this study. Based on the 3D horn failure model, the critical seismic acceleration coefficient of rock slopes was conducted with the modified Hoek–Brown (MHB) failure criterion in the framework of upper-bound theory for the first time. The nonlinear Hoek–Brown failure criterion is incorporated into the three-dimensional rotational failure mechanism, and a generalized tangent technique is introduced and employed to convert the nonlinear Hoek–Brown failure criterion into a linear criterion. The critical seismic acceleration coefficients obtained from this study were validated by the numerical simulation results based on finite element limit analysis. The agreement showed that the proposed method is effective. Finally, design charts were provided for exceptional cases for practical use in rock engineering.

Comparison of an improved self-consistent lower bound theory with Lehmann’s method for low-lying eigenvalues

Ritz eigenvalues only provide upper bounds for the energy levels, while obtaining lower bounds requires at least the calculation of the variances associated with these eigenvalues. The well-known Weinstein and Temple lower bounds based on the eigenvalues and variances converge very slowly and their quality is considerably worse than that of the Ritz upper bounds. Lehmann presented a method that in principle optimizes Temple’s lower bounds with significantly improved results. We have recently formulated a Self-Consistent Lower Bound Theory (SCLBT), which improves upon Temple’s results. In this paper, we further improve the SCLBT and compare its quality with Lehmann’s theory. The Lánczos algorithm for constructing the Hamiltonian matrix simplifies Lehmann’s theory and is essential for the SCLBT method. Using two lattice Hamiltonians, we compared the improved SCLBT (iSCLBT) with its previous implementation as well as with Lehmann’s lower bound theory. The novel iSCLBT exhibits a significant improvement over the previous version. Both Lehmann’s theory and the SCLBT variants provide significantly better lower bounds than those obtained from Weinstein’s and Temple’s methods. Compared to each other, the Lehmann and iSCLBT theories exhibit similar performance in terms of the quality and convergence of the lower bounds. By increasing the number of states included in the calculations, the lower bounds are tighter and their quality becomes comparable with that of the Ritz upper bounds. Both methods are suitable for providing lower bounds for low-lying excited states as well. Compared to Lehmann’s theory, one of the advantages of the iSCLBT method is that it does not necessarily require the Weinstein lower bound for its initial input, but Ritz eigenvalue estimates can also be used. Especially owing to this property the iSCLBT method sometimes exhibits improved convergence compared to that of Lehmann’s lower bounds

The lower bound of nonlocal gradient for non-convex and non-smooth image patches based regularization

In the inverse problem of image processing, we have witnessed that the non-convex and non-smooth regularizers can produce clearer image edges than convex ones such as total variation (TV). This fact can be explained by the uniform lower bound theory of the local gradient in non-convex and non-smooth regularization. In recent years, although it has been numerically shown that the nonlocal regularizers of various image patches based nonlocal methods can recover image textures well, we still desire a theoretical interpretation. To this end, we propose a non-convex non-smooth and block nonlocal (NNBN) regularization model based on image patches. By integrating the advantages of the non-convex and non-smooth potential function in the regularization term, the uniform lower bound theory of the image patches based nonlocal gradient is given. This approach partially explains why the proposed method can produce clearer image textures and edges. Compared to some classical regularization methods, such as total variation (TV), non-convex and non-smooth (NN) regularization, nonlocal total variation (NLTV) and block nonlocal total variation(BNLTV), our experimental results show that the proposed method improves restoration quality.

Comparison of an Improved Self-consistent Lower Bound Theory with Lehmann’s Method for Low-lying Eigenvalues

Ritz eigenvalues only provide upper bounds for the energy levels, while obtaining lower bounds requires at least the calculation of the variances associated with these eigenvalues. The well-known Weinstein and Temple lower bounds based on the eigenvalues and variances converge very slowly and their quality is considerably worse than that of the Ritz upper bounds. Lehmann presented a method that in principle optimizes Temple’s lower bounds with significantly improved results. We have recently formulated a Self-Consistent Lower Bound Theory (SCLBT), which improves upon Temple’s results. In this paper we further improve the SCLBT and compare its quality with Lehmann’s theory. The Lánczos algorithm for constructing the Hamiltonian matrix simplifies Lehmann’s theory and is essential for the SCLBT. Using two lattice Hamiltonians, we compared the improved SCLBT with its previous implementation as well as with Lehmann’s lower bound theory. The novel SCLBT exhibits a significant improvement over the previous version. Both Lehmann’s theory and the SCLBT provide significantly better lower bounds than those obtained from Weinstein’s and Temple’s methods. Compared to each other, the Lehmann and SCLBT theories exhibit similar performance in terms of the quality and convergence of the lower bounds. By increasing the number of states included in the calculations, the lower bounds are tighter and their quality becomes comparable with that of the Ritz upper bounds. Both methods are suitable for providing lower bounds for low-lying excited states as well. Compared to Lehmann’s theory, one of the advantages of the SCLBT method is that it does not necessarily require the Weinstein lower bound for its initial input, but Ritz eigenvalue estimates can also be used. Especially owing to this property the SCLBT method sometimes exhibits improved convergence compared to that of Lehmann’s lower bounds.

Calculation Method of Underground Cavern Loosening Pressure Based on Limit Analysis Using Upper-Bound Theory and Its Engineering Application

From the point of view of the failure mechanism of the disturbed zone, this paper uses the limit analysis upper-bound theory to analyze the calculation formula of the loosening pressure, distinguish the difference between the vertical pressure and the horizontal pressure in the underground cavern, combine the loosening characteristics of the disturbed zone with the open-type disturbed zone and the annular disturbed zone, and construct the multirigidity slider translation and rotation failure mode to discuss the calculation method of surrounding rock loosening pressure of underground caverns in upper soft and hard rock stratum. The relevant calculation examples are given, and the application of the upper-bound theory of limit analysis is demonstrated in detail. Based on the actual engineering background, the calculation results of the calculation method of the loosening pressure of the cavity based on the upper-bound theory of the limit analysis are analyzed and compared for the different depths and different types of caverns. The difference, rationality, and applicability of the calculation results of this method are analyzed and discussed.

Undrained seismic bearing capacity of strip footings horizontally embedded in two-layered slopes

This study investigated the undrained seismic bearing capacity of strip footings embedded in two-layered slopes by finite element limit analysis (FELA); in particular, a pseudostatic method was specified to seismic loads. Lower bound theory (LB), upper bound theory (UB), and adaptive meshing technique are employed for exploring the effect of the shear strength ratio of top layer and bottom layer, cu1/ cu2; the horizontal embedment depth of footings, b/ B; the footing locations (in bottom layer or top layer); seismic coefficient kh; and the slope gradient β on seismic bearing capacity. Results indicated that the seismic bearing capacity would increase with the growth of horizontal embedment depth of footings. The comparison between the predictions obtained from the proposed method and the existing method was presented, and the failure mechanisms are further summarized.

A Non-Culture-Bound Theory of Language Education

Educational linguistics is a dyadic science. The noun, linguistics, is a broad term which includes neuro-, psycho-, socio-, pragma-, ethno-linguistics and communication studies: areas where national ‘schools’ non longer exist. Educational, on the contrary, is a culture-bound term: language teaching is carried out according to laws which concern syllabi, exams and certifications, the language(s) of instruction, the teaching of the host language to migrant students, teacher training programmes etc. These juridical and administrative acts are meant for the local educational systems. We propose that it is possible to find a number of principles and models (we call them “hypotheses”) which can be accepted by culture-bound educational decision-makers, thus increasing consistency within language teaching and research throughout the world.

Effects of helicity on dissipation in homogeneous box turbulence

The dimensionless dissipation coefficient$\unicode[STIX]{x1D6FD}=\unicode[STIX]{x1D700}L/U^{3}$, where$\unicode[STIX]{x1D700}$is the dissipation rate,$U$the root-mean-square velocity and$L$the integral length scale, is an important characteristic of statistically stationary homogeneous turbulence. In studies of$\unicode[STIX]{x1D6FD}$, the external force is typically isotropic and large scale, and its helicity$H_{f}$either zero or not measured. Here, we study the dependence of$\unicode[STIX]{x1D6FD}$on$H_{f}$and find that it decreases$\unicode[STIX]{x1D6FD}$by up to 10 % for both isotropic forces and shear flows. The numerical finding is supported by static and dynamical upper bound theory. Both show a relative reduction similar to the numerical results. That is, the qualitative and quantitative dependence of$\unicode[STIX]{x1D6FD}$on the helicity of the force is well captured by upper bound theory. Consequences for the value of the Kolmogorov constant and theoretical aspects of turbulence control and modelling are discussed in connection with the properties of the external force. In particular, the eddy viscosity in large-eddy simulations of homogeneous turbulence should be decreased by at least 10 % in the case of strongly helical forcing.