Longitudinal mechanical response of tunnels under reverse faulting and its analytical solution

Abstract The Greenwood–Williamson (GW) model has been one of the commonly used contact models to study rough surface contact problems during the past decades. While this has been a successful model, it still has a number of restrictions: (i) surface asperities are spheres; (ii) the overall deformation must be assumed to be small enough, such that there is no interaction between asperities, i.e., they are independent of each other; and (iii) asperity deformation remains elastic. This renders the GW model unrealistic in many situations. In the present work, we resolve above restrictions in a discrete version of the GW model: instead of spherical asperities, we assumed that the surface consists of three-dimensional sinusoidal asperities which appear more similar to asperities on a rough surface. For single asperity mechanical response, we propose a Hertz-like analytical solution for purely elastic deformation and a semi-analytical solution based on finite element method (FEM) for elastic–plastic deformation. The asperity interaction is accounted for by discretely utilizing a modified Boussinesq solution without consideration of asperity merger. It is seen that the asperity interaction effect is more than just the delay of contact as shown in the statistical model, it also contributes to the loss of linearity between the contact force and the contact area. Our model also shows that: for elastic contact, using spherical asperities results in a larger average contact pressure than using sinusoids; when plasticity is taken into account, using a sphere to represent asperities results in a softer response as compared with using sinusoids. It is also confirmed that sinusoidal asperities are a much better description than spheres, by comparison with fully resolved FEM simulation results for computer-generated rough surfaces.

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A Simplified Analytical Solution of Mechanical Responses of Soil Subjected to Repeated Impact Loading

Mathematical Problems in Engineering ◽

10.1155/2020/6920535 ◽

2020 ◽

Vol 2020 ◽

pp. 1-10

Author(s):

Futian Zhao ◽

Jun Liu ◽

Zhimin Xiao ◽

Mingqing Liu ◽

Yue Wang ◽

...

Keyword(s):

Analytical Solution ◽

Dynamic Response ◽

Hollow Cylinder ◽

Impact Loading ◽

Dynamic Stress ◽

Mechanical Response ◽

Impact Load ◽

Projection Area ◽

Response Model ◽

Repeated Impact

A simplified dynamic response model is proposed based on the deformation and dynamic stress response characteristics of soil under impact loading. The foundation is divided into two distinct zones: a projection cylinder acting vertically under impact loading and a hollow cylinder outside the projection area. It is assumed that the ramming deformation of the projected cylinder under the vertical impact load is a quasi-static loading process under the maximum contact dynamic stress through the quasi-static method, and the settlement calculation without lateral deformation is given. It is assumed that the inner wall of the hollow cylinder is subjected to horizontal lateral pressure and the analytical solution of the horizontal dynamic stress considering the plastic deformation of soil is given. The simplified dynamic response model can reflect the mechanical response of soil under impulse train load well which can provide reference for similar projects.

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Mechanical Response of Plectonemic DNA: An Analytical Solution

Macromolecules ◽

10.1021/ma702713x ◽

2008 ◽

Vol 41 (12) ◽

pp. 4479-4483 ◽

Cited By ~ 32

Author(s):

N. Clauvelin ◽

B. Audoly ◽

S. Neukirch

Keyword(s):

Analytical Solution ◽

Mechanical Response

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Formulation of a three dimensional analytical solution to evaluate stresses in backfilled vertical narrow openings

Canadian Geotechnical Journal ◽

10.1139/t05-084 ◽

2005 ◽

Vol 42 (6) ◽

pp. 1705-1717 ◽

Cited By ~ 65

Author(s):

Li Li ◽

Michel Aubertin ◽

Tikou Belem

Keyword(s):

Numerical Modeling ◽

Analytical Solution ◽

Analytical Solutions ◽

Mechanical Response ◽

Three Dimensional ◽

Earth Pressure ◽

The State ◽

Experimental Results ◽

State Of Stress ◽

Earth Pressures

The mechanical response of backfill in narrow openings is significantly influenced by its interaction with the surrounding walls. Previous work conducted on backfilled trenches and mining stopes indicates that the theory of arching can be used to estimate earth pressures in narrow, vertical backfilled openings. In this paper, a 3D analytical solution is proposed to evaluate the state of stress along the boundaries of the openings. The proposed solution, based on a generalized version of the Marston approach, is compared with numerical modeling and laboratory experimental results taken from the literature. A discussion follows on some particular features and limitations of the analytical solutions.Key words: backfill, earth pressure, 3D openings, analytical solutions, trenches, mining stopes.

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Thermal Stress Analysis for Bi-modulus Foundation Beam under Nonlinear Temperature Difference

International Journal of Computational Methods ◽

10.1142/s0219876217500244 ◽

2017 ◽

Vol 14 (01) ◽

pp. 1750024 ◽

Cited By ~ 1

Author(s):

Jinling Gao ◽

Wenjuan Yao

Keyword(s):

Finite Element ◽

Analytical Solution ◽

Mechanical Response ◽

Bending Moment ◽

Neutral Axis ◽

Calculation Procedure ◽

Winkler Foundation ◽

Linear Temperature ◽

Finite Element Software ◽

Nonlinear Temperature

It is shown that many materials in practical engineering have different moduli in tension and compression. Especially, graphene, a magical material with the highest strength, is a kind of bi-modulus material. In this paper, mechanical response of bi-modulus Winkler foundation beam under nonlinear temperature distribution along height of the beam is studied. A new and convenient method, “intersecting line criterion”, is proposed to certify number of neutral axis in foundation beam and governing equation (set) of position of neutral axis is established, which is solved by iteration procedure of Newton’s method in Matlab. Semi-analytical solutions of stress, deflection and bending moment are subsequently obtained. Meanwhile, a finite element calculation procedure for calculating the temperature stress in bi-modulus structures is developed. Return the analytical solution to the result of the same modulus theory, and compare the analytical solution with finite element procedure solution and common finite element software Abaqus simulation solution. It shows that both of semi-analytical solution and calculation procedure proposed are reliable to use. Finally, discrepancies between nonlinear temperature effect and linear temperature and external force effect are discussed, which may supply some suggestions for calculation and optimization of such structures and members.

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Study on an Analytical Solution to the Mechanical Response of Soil Cut by a Bionic Force Enhancement Grouser

Journal of Marine Science and Engineering ◽

10.3390/jmse9121401 ◽

2021 ◽

Vol 9 (12) ◽

pp. 1401

Author(s):

Yanli Chen ◽

Wei Zhu ◽

Wengang Qi ◽

Wenbo Ma

Keyword(s):

Analytical Solution ◽

Deep Sea ◽

Mechanical Response ◽

Soft Soil ◽

Earth Pressure ◽

Mineral Resources ◽

Difficult Problem ◽

Enhancement Effect ◽

Force Enhancement ◽

Tractive Force

With the depletion of land mineral resources, people have turned their attention to the sea. As an important part of deep-sea mining systems, the technical research and development of ore collectors has always been a difficult problem in many countries. According to the characteristic that buffalo hoof is suitable for walking on soft soil, a kind of bionic grouser for a deep-sea mining vehicle is designed in this paper. Through the optimization of Rankine’s passive earth pressure theory, the formula for calculating the tractive force of the grouser is obtained. The accuracy of the analytical solution is verified by finite element simulation, and the force enhancement mechanism of the bionic grouser is revealed. The results show that the design of the bionic grouser has a significant effect on the improvement of tractive force, and the tractive force of the No. 1 bionic grouser is 17.52% higher than that of the straight grouser. On this basis, the geometric parameters of the bionic grouser profile are optimized. The results show that when L is 0 mm and R is 183 mm, the force enhancement effect reaches the maximum of 27%, which provides a design basis for optimizing the grouser and improving the mining efficiency of the collector.

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Comparison of Substructures Between Uniaxial and Biaxial Deformation in 1100-0 Aluminum

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100096989 ◽

1981 ◽

Vol 39 ◽

pp. 52-53

Author(s):

D. L. Rohr ◽

S. S. Hecker

Keyword(s):

Plastic Strain ◽

Cell Walls ◽

Room Temperature ◽

Mechanical Response ◽

Biaxial Tension ◽

Initial Deformation ◽

Uniaxial Deformation ◽

Biaxial Deformation ◽

Stress States ◽

Comprehensive Study

As part of a comprehensive study of microstructural and mechanical response of metals to uniaxial and biaxial deformations, the development of substructure in 1100 A1 has been studied over a range of plastic strain for two stress states.Specimens of 1100 aluminum annealed at 350 C were tested in uniaxial (UT) and balanced biaxial tension (BBT) at room temperature to different strain levels. The biaxial specimens were produced by the in-plane punch stretching technique. Areas of known strain levels were prepared for TEM by lapping followed by jet electropolishing. All specimens were examined in a JEOL 200B run at 150 and 200 kV within 24 to 36 hours after testing.The development of the substructure with deformation is shown in Fig. 1 for both stress states. Initial deformation produces dislocation tangles, which form cell walls by 10% uniaxial deformation, and start to recover to form subgrains by 25%. The results of several hundred measurements of cell/subgrain sizes by a linear intercept technique are presented in Table I.

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Construction of plastic contact deformation maps on ceramics: a case study on aluminum nitride

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100165641 ◽

1996 ◽

Vol 54 ◽

pp. 636-637

Author(s):

D. L. Callahan

Keyword(s):

Plastic Deformation ◽

Aluminum Nitride ◽

Mechanical Response ◽

Three Dimensional ◽

Bright Field Image ◽

Perfectly Plastic ◽

Contrast Analysis ◽

Deformation Patterns

Modern polishing, precision machining and microindentation techniques allow the processing and mechanical characterization of ceramics at nanometric scales and within entirely plastic deformation regimes. The mechanical response of most ceramics to such highly constrained contact is not predictable from macroscopic properties and the microstructural deformation patterns have proven difficult to characterize by the application of any individual technique. In this study, TEM techniques of contrast analysis and CBED are combined with stereographic analysis to construct a three-dimensional microstructure deformation map of the surface of a perfectly plastic microindentation on macroscopically brittle aluminum nitride.The bright field image in Figure 1 shows a lg Vickers microindentation contained within a single AlN grain far from any boundaries. High densities of dislocations are evident, particularly near facet edges but are not individually resolvable. The prominent bend contours also indicate the severity of plastic deformation. Figure 2 is a selected area diffraction pattern covering the entire indentation area.

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