The field monitoring experiment of the high-level key stratum movement in coal mining based on collaborative DOFS and MPBX

The deformation and movement characteristics of high-level key stratums in overlying strata are important for estimating ground subsidence and understanding failure characteristics of ultrathick strata during mining. In this study, a distributed optical fiber sensor (DOFS) and multipoint borehole extensometers (MPBXs) were collaboratively employed to monitor the deformation of high-level key stratums in situ during the mining process at working face 130,604 of the Maiduoshan Coal Mine. DOFS monitoring results showed that the distance from advance influence of mining on the ground surface is 219.2 m. The deformation of the shallow stratums were greater and was affected earlier than that of the deep stratums. The deformation in the strata did not occur continuously and the boundary curve of the impact from advance mining was not a straight line with the advancement of the working face. By the MPBX technology, we measured the strata movement and obtained four-stage characteristics of high-level key stratum movement. The subsidence of the primary key stratum and the sub key stratum were monitored to reach 1389 and 1437 mm; their final relative displacement differed by 48 mm. No bed separation was observed in between the strata, and the key stratums tended to sink as a whole with the advancement of the working face. This research guides the analysis the movement of thick high-level key stratums.

Construction of C1 Rational Bi-Quartic Spline With Positivity-Preserving Interpolation: Numerical Results and Analysis

From the observed datasets, we should be able to produce curve surfaces that have the same characteristics as the original datasets. For instance, if the given data are positive, then the resulting curve or surface must be positive on entire given intervals, i.e., everywhere. In this study, a new partial blended rational bi-quartic spline with C1 continuity is constructed through the partially blended scheme. This rational spline is defined on four corners of the rectangular meshes. The sufficient condition for the positivity of rational bi-quartic spline is derived on four boundary curve networks. There are eight free parameters that can be used for shape modification. The first-order partial derivatives are estimated by using numerical techniques. We also show that the proposed scheme is local quadratic reproducing such that it can exactly reproduce the quadratic surface. We test the proposed scheme to interpolate various types of positive surface data. Based on statistical indicators such as the root mean square error (RMSE) and coefficient of determination (R2), we found that the proposed scheme is on par with some established schemes. In fact, it requires less CPU times (in seconds) to generate the interpolating surface on rectangular meshes. Furthermore, by combining the statistical indicators’ result and graphically visualizing the test functions, the proposed method has the capability to reconstruct very comparable smoothing interpolating positive surfaces compared to some existing schemes. This finding is significant in producing a better interpolating surface for computer graphics applications since the proposed scheme has a smaller error compared with existing schemes.

Eigenvalue Estimates via Pseudospectra

In this note, given a matrix A∈Cn×n (or a general matrix polynomial P(z), z∈C) and an arbitrary scalar λ0∈C, we show how to define a sequence μkk∈N which converges to some element of its spectrum. The scalar λ0 serves as initial term (μ0=λ0), while additional terms are constructed through a recursive procedure, exploiting the fact that each term μk of this sequence is in fact a point lying on the boundary curve of some pseudospectral set of A (or P(z)). Then, the next term in the sequence is detected in the direction which is normal to this curve at the point μk. Repeating the construction for additional initial points, it is possible to approximate peripheral eigenvalues, localize the spectrum and even obtain spectral enclosures. Hence, as a by-product of our method, a computationally cheap procedure for approximate pseudospectra computations emerges. An advantage of the proposed approach is that it does not make any assumptions on the location of the spectrum. The fact that all computations are performed on some dynamically chosen locations on the complex plane which converge to the eigenvalues, rather than on a large number of predefined points on a rigid grid, can be used to accelerate conventional grid algorithms. Parallel implementation of the method or use in conjunction with randomization techniques can lead to further computational savings when applied to large-scale matrices.

Reconstruction of Two-dimensional Image to Three-dimensional Point Cloud Data for Detection of Empty Rot Defects in Tree Growth

In the application of nondestructive detecting of trees, it is a technical problem to use radar waves to detect tree specimens with growth defects, how to segment defect areas after obtaining two-dimensional images, and reverse simulate the detection results with three-dimensional point cloud data. Therefore, the method of extracting boundary information according to color features is studied to extract the boundary curve of empty rot area, and the selection of higher precision extraction algorithm is determined by comparing the boundary extraction results of HSV color space and RGB color space in laboratory According to the extracted void boundary curve, the reverse modeling is carried out, and the mapping from 2D inspection gray image to 3D space is realized, The point cloud data reconstruction needed for 3D modeling of multi-curved surfaces is obtained in reverse. The boundary curve extraction algorithm in this study is used to process the images of nondestructive testing of trees. Through comparative experiments and error analysis, the accurate modeling conclusion from inversion of 2D images to 3D point cloud data reconstruction by radar wave detection is verified, and the Core issue problem of point cloud reconstruction in the ill-conditioned area of tree growth and decay detected by radar wave is solved.

Backbone curves, Neimark-Sacker boundaries and appearance of quasi-periodicity in nonlinear oscillators: application to 1:2 internal resonance and frequency combs in MEMS

Quasi-periodic solutions can arise in assemblies of nonlinear oscillators as a consequence of Neimark-Sacker bifurcations. In this work, the appearance of Neimark-Sacker bifurcations is investigated analytically and numerically in the specific case of a system of two coupled oscillators featuring a 1:2 internal resonance. More specifically, the locus of Neimark-Sacker points is analytically derived and its evolution with respect to the system parameters is highlighted. The backbone curves, solution of the conservative system, are first investigated, showing in particular the existence of two families of periodic orbits, denoted as parabolic modes. The behaviour of these modes, when the detuning between the eigenfrequencies of the system is varied, is underlined. The non-vanishing limit value, at the origin of one solution family, allows explaining the appearance of isolated solutions for the damped-forced system. The results are then applied to a Micro-Electro-Mechanical System-like shallow arch structure, to show how the analytical expression of the Neimark-Sacker boundary curve can be used for rapid prediction of the appearance of quasiperiodic regime, and thus frequency combs, in Micro-Electro-Mechanical System dynamics.

Strata and Surface Influence Range of Deep Coal Mining for Mine Land Reuse

The rational assessment and determination of strata and surface influence range of underground coal mining is straightly associated to the safe production of the wellbore, the reuse of mine land and the regional development. With the depth of coal mining in the world increasing, if the boundary curve of strata and surface movement continues to be considered as a straight line, there will be a great deviation from the real situation, which will seriously waste the land resources of mining area. To solve this issue, the numerical simulation methods were employed to investigate the stratum and surface movement boundary curves of deep caving and backfilling mining in this paper. The findings indicated that: 1) The strata and surface movement boundary of deep caving and backfilling mining were all curves, and they were in accordance with the exponential function, but the influence range of strata and surface movement of deep different mining methods were different; 2) The backfilling rate of deep backfilling mining had an influence on movement boundary of strata and surface. With the backfilling rate decreasing, the influence range of strata and surface movement boundary were increased. 3) The research results were applied to a case in order to confirm the new methods for determining the influence range of strata and surface movement of deep mining. Example application shows that the safe production of the wellbore not only can be guaranteed, but also the reuse area of the mine field can be enhanced.

THEORETICAL SOLUTION OF PILING COMPACTION AND THE INFLUENCE OF PILE-SOIL-BOUNDARY CURVE HYPOTHESIS

Research is ongoing to find theoretical solution to three-dimensional piling compaction. Considering the spacial-axis-symmetric characteristics, the boundary surface of pile-soil interaction is expressed by polynomials of different orders. First, the curve family parameter is introduced to construct the displacement and integral function. Then, the solution of pile-soil interaction is derived by combining the constitutive relation model of Duncan-Chang and the variational theory. Results of engineering computing show that the theoretical solution converges to the classical CEM and the limit equilibrium theory well at the corresponding computing area. Moreover, the effects of polynomial of different orders on the calculation results are not obvious. The conclusion in this paper can be used for reference in the derivation and application for other interaction of structure and soil problems.

Theoretical Analysis of Mining Induced Overburden Subsidence Boundary with the Horizontal Coal Seam Mining

The overburden subsidence induced by underground mining has caused great damage to the ecological environmental and seriously threatens the safe use of underground structures. Focusing on the overburden subsidence, this paper uses theoretical analysis method to study the overburden subsidence boundary with a horizontal coal seam mining. In this paper, the viscoelastic theory and the random medium theory are used separately to deduce and analyze the subsidence boundary of bedrock and unconsolidated stratum, which are two media with different lithology. For bedrock, the results show that the subsidence boundary of bedrock is 1/4 of the wavelength of pressure wave from the mining boundary, strata subsidence boundary expands with the increase of vertical distance between calculated strata and coal seam, and the subsidence boundary in bedrock is an upward concave curve. For unconsolidated stratum, the results show that the larger the internal friction angle, the greater the angle between subsidence boundary and horizontal line. From the bottom to the surface of the unconsolidated stratum, the internal friction angle decreases gradually and the angle between subsidence boundary and horizontal line also decreases gradually, so the subsidence boundary curve in the unconsolidated stratum is convex. Combined with the bedrock and unconsolidated stratum, it is concluded that the subsidence boundary of the whole overburden is bowl-shaped. This study is helpful to reveal the black box of rock subsidence and can provide theoretical support for the establishment of overburden subsidence prediction model and transparent mine in the later stage.

Damage Analysis of Composite CFRP Tubes Using Acoustic Emission Monitoring and Pattern Recognition Approach

The acoustic emission method has been adopted for detection of damage mechanisms in carbon-fiber-reinforced polymer composite tubes during the three-point bending test. The damage evolution process of the individual samples has been monitored using the acoustic emission method, which is one of the non-destructive methods. The obtained data were then subjected to a two-step technique, which combines the unsupervised pattern recognition approach utilizing the short-time frequency spectra with the boundary curve enabling the already clustered data to be additionally filtered. The boundary curve identification has been carried out on the basis of preliminary tensile tests of the carbon fiber sheafs, where, by overlapping the force versus time dependency by the acoustic emission activity versus time dependency, it was possible to identify the boundary which will separate the signals originating from the fiber break from unwanted secondary sources. The application of the presented two-step method resulted in the identification of the failure mechanisms such as matrix cracking, fiber break, decohesion, and debonding. Besides the comparison of the results with already published research papers, the study presents the comprehensive parametric acoustic emission signal analysis of the individual clusters.

Liquefaction Analysis using Shear Wave Velocity

The Andrus and Stokoe curves developed based on shear wave velocity case history databases, are the most widely used in the context of the Seed and Idriss simplified procedure as a deterministic model. Theses curves were developed from the database according to the calculate cyclic stress ratio (CSR) proposed by Seed and Idriss in 1971 with the assumption that the dynamic cyclic shear stress (τd) is always less than the simplified cyclic shear stress (τr) deduced by Seed and Idriss based on their simplifying hypotheses (rd= τd / τr <1). Filali and Sbartai in 2017, showed that rd can in many cases be greater than 1, and they have proposed a correction for the CSR in the range where rd >1. In this paper, we will present a probabilistic study based on the Bayesian method for the evaluation of the liquefaction potential of a soil deposit using a case history database based on shear wave velocity measurement. The result of this analysis shows that by using the corrected version of the simplified method, the boundary curve is moved to a new position. Then, the objective of this study is to present an adjusted mathematical model which characterizes the new position of the boundary curve (CRR) and a new formulation for computing the probability of liquefaction based on the probabilistic shape of the CRR curves using the corrected and the original version of the simplified method.