A novel measurement method of toe debris thickness for bored piles based on one-dimensional wave theory

The existence of toe debris at the bottom of the bored pile will reduce the bearing capacity of the pile. This paper develops a novel equipment to measure the thickness of toe debris for bored piles. The equipment consists of a test rod, test hammer, velocimeter, transmission cable and data receiving and processing device. Based on the one-dimensional wave theory, the mechanism of the sudden change of the velocity time curve received at the top of the test rod is analyzed, which is caused by the change of the wave impedance at the interface between the test rod and the sediment, thus the feasibility of the equipment is verified in theory. Finally, numerical simulations of toe debris under various working conditions are carried out to verify the reliability of the equipment. The results show that the test curves are sensitive to the materials of test rod using proposed equipment when the thickness of toe debris is equal or greater than 50 cm, and the test values are all larger than actual values, which meet the requirement of relevant specifications. The test results are more accuracy when the thickness of toe debris is less than 50 cm. when the excited force is large, not only the sudden change is easy to be discriminated, but also the test accuracy can be assured. The remainder toe debris meet the requirement of relevant specifications after clearing pile hole according the proposed method. And the device is not affected by the properties of the sediment material, which indicates that the proposed equipment can perform well to test the thickness of toe debris

The Reduced Order Method for Solving the Linear Complementarity Problem with an M-Matrix

In this paper, by seeking the zero and the positive entry positions of the solution, we provide a direct method, called the reduced order method, for solving the linear complementarity problem with an M-matrix. By this method, the linear complementarity problem is transformed into a low order linear complementarity problem with some low order linear equations and the solution is constructed by the solution of the low order linear complementarity problem and the solutions of these low order linear equations in the transformations. In order to show the accuracy and the effectiveness of the method, the corresponding numerical experiments are performed

Hybrid Topological Superconductivity and Hinge Majorana Flat Band in Type-II Dirac Semimetals

Type-II Dirac semimetals (DSMs) have a distinct Fermi surface topology, which allows them to host novel topological superconductivity (TSC) different from type-I DSMs. Depending on the relationship between intra- and inter-orbital electron-electron interactions, the phase diagram of superconductivity is obtained in type-II DSMs. We find that when the inter-orbital attraction is dominant, an unconventional inter-orbital intra-spin superconducting (SC) state ($B_{1u}$ and $B_{2u}$ pairing channels of $D_{4h}$ point group) is realized, yielding hybrid TSC, i.e., first- and second-order TSC exists at the same time. Further analysis reveals the Majorana flat bands on the $z$-directed hinges, which penetrate through the whole hinge Brillouin zone and link the projections of the surface helical Majorana cones at time-reversal-invariant momenta. These higher-order hinge modes are symmetry-protected and can even host strong stability against finite $C_{4z}$ rotation symmetry-breaking order. We suggest that experimental realization of these findings can be explored in transition metal dichalcogenides