Case study on the mechanics of NPR anchor cable compensation for large deformation tunnel in soft rock in the Transverse Mountain area,China

A study was conducted to analyze the deformation mechanism of strongly weathered quartz schist in the Daliangshan Tunnel,located in the western Transverse Mountain area.A large deformation problem was experienced during the tunnel construction.To mitigate this problem,a support system was designed incorporating negative Poisson ratio(NPR)anchor cables with negative Poisson ratio effect.Physical model experiments,field experiments,and numerical simulation experiments were conducted to investigate the compensation mechanical behavior of NPR anchor cables.The large deformations of soft rocks in the Daliangshan Tunnel are caused by a high ground stress,a high degree of joint fracture development,and a high degree of surrounding rock fragmentation.A compensation mechanics support system combining long and short NPR anchor cables was suggested to provide sufficient counter-support force(approximately 350 kN)for the surrounding rock inside the tunnel.Comparing the NPR anchor cable support system with the original support system used in the Daliangshan tunnel showed that an NPR anchor cable support system,combining cables of 6.3 m and 10.3 m in length,effectively prevented convergence of surrounding rock deformation,and the integrated settlement convergence value remained below 300 mm.This study provides an effective scientific basis for resolving large deformation problems in deeply buried soft rocks in western transverse mountain areas.

Topology Optimization of Metamaterial Microstructures for Negative Poisson’s Ratio under Large Deformation Using a Gradient-Free Method

Negative Poisson’s ratio(NPR)metamaterials are attractive for their unique mechanical behaviors and potential applications in deformation control and energy absorption.However,when subjected to significant stretching,NPR metamaterials designed under small strain assumption may experience a rapid degradation in NPR performance.To address this issue,this study aims to design metamaterials maintaining a targeted NPR under large deformation by taking advantage of the geometry nonlinearity mechanism.A representative periodic unit cell is modeled considering geometry nonlinearity,and its topology is designed using a gradient-free method.The unit cell microstructural topologies are described with the material-field series-expansion(MFSE)method.The MFSE method assumes spatial correlation of the material distribution,which greatly reduces the number of required design variables.To conveniently design metamaterials with desired NPR under large deformation,we propose a two-stage gradient-free metamaterial topology optimization method,which fully takes advantage of the dimension reduction benefits of the MFSE method and the Kriging surrogate model technique.Initially,we use homogenization to find a preliminary NPR design under a small deformation assumption.In the second stage,we begin with this preliminary design and minimize deviations in NPR from a targeted value under large deformation.Using this strategy and solution technique,we successfully obtain a group of NPR metamaterials that can sustain different desired NPRs in the range of[−0.8,−0.1]under uniaxial stretching up to 20% strain.Furthermore,typical microstructure designs are fabricated and tested through experiments.The experimental results show good consistency with our numerical results,demonstrating the effectiveness of the present gradientfree NPR metamaterial design strategy.

Excavation compensation theory and supplementary technology system for large deformation disasters

Given the challenges in managing large deformation disasters in energy engineering,traffic tunnel engineering,and slope engineering,the excavation compensation theory has been proposed for large deformation disasters and the supplementary technology system is developed accordingly.This theory is based on the concept that“all destructive behaviors in tunnel engineering originate from excavation.”This paper summarizes the development of the excavation compensation theory in five aspects:the“theory,”“equipment,”“technology,”the design method with large deformation mechanics,and engineering applications.First,the calculation method for compensation force has been developed based on this theory,and a comprehensive large deformation disaster control theory system is formed.Second,a negative Poisson's ratio anchor cable with high preload,large deformation,and super energy absorption characteristics has been independently developed and applied to large deformation disaster control.An intelligent tunnel monitoring and early warning cloud platform system are established for remote monitoring and early warning system of Newton force in landslide geological hazards.Third,the double gradient advance grouting technology,the two-dimensional blasting technology,and the integrated Newton force monitoring--early warning--control technology are developed for different engineering environments.Finally,some applications of this theory in China's energy,traffic tunnels,landslide,and other field projects have been analyzed,which successfully demonstrates the capability of this theory in large deformation disaster control.

Anchorage performance of large-diameter FRP bolts and their application in large deformation roadway

In underground coal mines, fibre reinforced polymer(FRP) bolt is ideal for mined rib reinforcements as it can prevent gas explosions caused by shearer frictional spark. With increasing mining depth, small diameter FRP bolts used in shallow underground mining cannot fulfil the rib support requirements. Under the engineering background of deep underground shortwall mining in Wudong coal mine, this paper systematically studies Φ27 mm FRP bolt support for large deformation coal rib. Specimens with a fan-shaped cross-section were used to enable the tensile testing of the bolt rod, the measured average tensile strength of the studied FRP bolt was(486.1 ± 9.6) MPa with a maximum elongation of 5.7%±0.6%.The shear strength of the bolt was measured as approximately 258 MPa using a self-made double shear testing apparatus. Based on the equivalent radial stiffness principle, a laboratory short encapsulation pullout test(SEPT) method for rib bolting has been developed undertaken consideration of the mechanical properties of the coal seam. Results showed that the average peak anchorage forces of the Φ27 mm FRP bolt and Φ20 mm steel rebar bolt were 108.4 and 66.4 k N, respectively, which were agreed with the theoretical calculations and field measurements. Based on theoretical analysis of the loading states of the bolt under site conditions, bolting method of full-length resin grouting was adopted to offset the weaknesses of the FRP bolt. Numerical method was employed to compare the bolting effect using Φ27 mm FRP bolts and steel rebar bolts. Large diameter FRP bolting was determined as the optimum rib support scheme to increase the productivity of the coal mine and to enhance the ground control capability for+425 level mining roadways. This study provides the laboratory testing design and theoretical prediction of large diameter FRP bolts used for rib support in large deformation roadways.

Numerical simulation of rockburst disaster and control strategy of constant resistance and large deformation anchor cable in Gaoloushan tunnel

The Gaoloushan Tunnel in Longnan City,Gansu Province,China,frequently experiences rockburst disasters due to high in-situ stress.Managing rockburst in deep-buried tunnels remains a challenging issue.This paper employs RFPA(Rock Failure Process Analysis)software to establish a calculation model of constant resistance and large deformation(CRLD)anchorages and analyzes the effects of different support methods and pre-stress levels on rockburst.We simulate the process of tunnel rockburst disasters and find that ordinary anchor support incurs rockburst on the right arch waist and arch top,forming a V-shaped explosion pit.CRLD anchor support has several advantages in rockburst control,such as more uniform stress distribution in the surrounding rock,a uniform distribution of plastic zones,less noticeable damage to the tunnel,and effective control of the arch top displacement.The effectiveness of the CRLD anchor support under varying pre-stress conditions shows that a higher prestress results in a smaller plastic zone of the surrounding rock and arch top displacement and a lower number of acoustic emission signals,which better explains the excavation compensation effect.Moreover,adding long anchorages in the deep surrounding rock area can better control rockburst and reduce surrounding rock deformation.Based on these findings,we propose a comprehensive control system that combines long and short anchorages and provides the optimal scheme based on calculations.Therefore,by using high-prestress CRLD anchor support and the combination of long and short anchorages at critical positions,we can enhance the integrity of the surrounding rock,effectively absorb the energy released by the surrounding rock deformation,and reduce the incidence of rockburst disasters.

Compensation excavation method control for large deformation disaster of mountain soft rock tunnel

In recent years,the mine tunneling method and the new Austrian tunneling method have been considered the main theories of tunneling approaches in China.It is difficult for the traditional technique to overcome the large deformation problems imposed by complex geological conditions of mountain soft rock tunneling.Hence,the compensation excavation method has been proposed to solve this issue under the consideration that all damage in tunneling originates from the excavation.It uses supportive strategies to counteract the excavation effects successfully.This paper provides an overview of the fundamental ideas of the compensation excavation method,methodologies,and field applications.The scientific validity and feasibility of the compensation excavation method were investigated through the practical engineering study of the Muzhailing and Changning tunnels.

Two-Dimensional Large Deformation Finite Element Analysisfor the Pulling-up of Plate Anchor

Based on mesh regeneration and stress interpolation from an old mesh to a new one, a large deformation finite element model is developed for the study of the behaviour of circular plate anchors subjected to uplift loading. For the deterruination of the distributions of stress components across a clay foundation, the Recovery by Equilibrium in Patches is extended to plastic analyses. ABAQUS, a commercial finite element package, is customized and linked into our program so as to keep automatic and efficient running of large deformation calculation. The quality of stress interpolation is testified by evaluations of Tresca stress and nodal reaction forces. The complete pulling-up processes of plate anchors buried in homogeneous clay arc simulated, and typical pulling force-displacement responses of a deep anchor and a shallow anchor are compared. Different from the results of previous studies, large deformation analysis is of the capability of estimating the breakaway between the anchor bottom and soils. For deep anchors, the variation of mobilized uplift resistance with anchor settlement is composed of three stages, and the initial buried depths of anchors affect the separation embedment slightly. The uplift bearing capacity of deep anchors is usually higher than that of shallow anchors.

Nonlinear formulation for flexible multibody system with large deformation

In this paper, nonlinear modeling for flexible multibody system with large deformation is investigated. Absolute nodal coordinates are employed to describe the displacement, and variational motion equations of a flexible body are derived on the basis of the geometric nonlinear theory, in which both the shear strain and the transverse normal strain are taken into account. By separating the inner and the boundary nodal coordinates, the motion equations of a flexible multibody system are assembled. The advantage of such formulation is that the constraint equations and the forward recursive equations become linear because the absolute nodal coordinates are used. A spatial double pendulum connected to the ground with a spherical joint is simulated to investigate the dynamic performance of flexible beams with large deformation. Finally, the resultant constant total energy validates the present formulation.

Application of MLPG in large deformation analysis

Two-dimensional large deformation analysis of hyperelastic and elasto-plastic solids based on the Meshless Local Petrov-Galerkin method （MLPG） is presented. A material configuration based the nonlinear MLPG formulation is introduced for the large deformation analysis of both path-dependent and path-independent materials. The supports of the MLS approximation functions cover the same sets of nodes during material deformation, thus the shape function needs to be computed only in the initial stage. The multiplicative hyperelasto-plastic constitutive model is adopted to avoid objective time integration for stress update in large rota- tion. With this constitutive model, the computational formulations for path-dependent and path-independent materials become identical. Computational efficiency of the nonlinear MLPG method is discussed and optimized in several aspects to make the MLPG an O（N） algorithm. The numerical examples indicate that the MLPG method can solve large deformation problems accurately. Moreover, the MLPG computations enjoy better convergence rate than the FEM under very large particle distortion.

Isogeometric analysis of free-form Timoshenko curved beams including the nonlinear effects of large deformations

In the present paper, the isogeometric analysis（IGA） of free-form planar curved beams is formulated based on the nonlinear Timoshenko beam theory to investigate the large deformation of beams with variable curvature. Based on the isoparametric concept, the shape functions of the field variables（displacement and rotation） in a finite element analysis are considered to be the same as the non-uniform rational basis spline（NURBS） basis functions defining the geometry. The validity of the presented formulation is tested in five case studies covering a wide range of engineering curved structures including from straight and constant curvature to variable curvature beams. The nonlinear deformation results obtained by the presented method are compared to well-established benchmark examples and also compared to the results of linear and nonlinear finite element analyses. As the nonlinear load-deflection behavior of Timoshenko beams is the main topic of this article, the results strongly show the applicability of the IGA method to the large deformation analysis of free-form curved beams. Finally, it is interesting to notice that, until very recently, the large deformations analysis of free-form Timoshenko curved beams has not been considered in IGA by researchers.

Numerical modeling of large deformation and nonlinear frictional contact of excavation boundary of deep soft rock tunnel

Roadways excavated in soft rocks at great depth are difficult to be maintained due to large deformation of surrounding rocks, which greatly influences the safety and efficiency of deep resources exploitation. During the excavation process of a deep soft rock tunnel, the rock wall may be compacted due to large deformation. In this paper, the technique to address this problem by a two-dimensional (2D) finite element software, large deformation engineering analyses software (LDEAS 1.0), is provided. By using the Lagrange multiplier method, the kinematic constraint of non-penetrating condition and static constraint of Coulomb friction are introduced to the governing equations in the form of incremental displacement. The numerical example demonstrates the efficiency of this technology. Deformations of a transportation tunnel in inclined soft rock strata at the depth of 1 000 m in Qishan coal mine and a tunnel excavated to three different depths are analyzed by two models, i.e. the additive decomposition model and polar decomposition model. It can be found that the deformation of the transportation tunnel is asymmetrical due to the inclination of rock strata. For extremely soft rock, large deformation can converge only for the additive decomposition model. The deformation of surrounding rocks increases with the increase in the tunnel depth for both models. At the same depth, the deformation calculated by the additive decomposition model is smaller than that by the polar decomposition model.

Experimental analysis of crack tip fields in rubber materials under large deformation

A three-nested-deformation model is proposed to describe crack-tip fields in rubber-like materials with large deformation. The model is inspired by the distribution of the measured in-plane and out-of-plane deformation. The in- plane displacement of crack-tip fields under both Mode 1 and mixed-mode （Mode I-II） fracture conditions is measured by using the digital Moir6 method. The deformation character- istics and experimental sector division mode are investigated by comparing the measured displacement fields under differ- ent fracture modes. The out-of-plane displacement field near the crack tip is measured using the three-dimensional digital speckle correlation method.

The effect of large deformation and material nonlinearity on gel indentation

A gel, an aggregate of polymers with solvents, has dual attributes of solid and liquid as solvent migrates in and out of the polymer network. Indentation has recently been used to characterize the mechanical properties of gels. This paper evaluates the effects of large deformation and material nonlinearity on gel indentation through theoretical modeling and finite element analysis. It is found that large deformation significantly affects the interpretation of the experimen- tal observations and the classical relation between indenta- tion force and depth has limitations for large deformation. The material nonlinearity does not play a very important role on indentation experiment so that the poroelasticity is a good approximation. Based on these observations, this paper proposes an alternative approach to measure the mechanical properties of gels, namely, uniaxial compression experiment.

Large Deformation Analysis and Synthesis of Elastic Closed-loop Mechanism Made of a Certain Spring Wire Described by Free Curves

Recently novel mechanisms with compact size and without many mechanical elements such as bearing are strongly required for medical devices such as surgical operation devices. This paper describes analysis and synthesis of elastic link mechanisms of a single spring beam which can be manufactured by NC coiling machines. These mechanisms are expected as disposable micro forceps. Smooth Curvature Model（SCM） with 3rd order Legendre polynomial curvature functions is applied to calculate large deformation of a curved cantilever beam by taking account of the balance between external and internal elastic forces and moments. SCM is then extended to analyze large deformation of a closed-loop curved elastic beam which is composed of multiple free curved beams. A closed-loop elastic link is divided into two free curved cantilever beams each of which is assumed as serially connected free curved cantilever beams described with SCM. The sets of coefficients of Legendre polynomials of SCM in all free curved cantilever beams are determined by taking account of the force and moment balance at connecting point where external input force is applied. The sets of coefficients of Legendre polynomials of a nonleaded closed-loop elastic link are optimized to design a link mechanism which can generate specified output motion due to input force applied at the assumed dividing point. For example, two planar micro grippers with a single pulling input force are analyzed and designed. The elastic deformation analyzed with proposed method agrees very well with that calculated with FEM. The designed micro gripper can generate the desired pinching motion. The proposed method can contribute to design compact and simple elastic mechanisms without high calculation costs.

Large deformation simulations of geomaterials using moving particle semi-implicit method

Numerical simulation tools are required to describe large deformations of geomaterials for evaluating the risk of geo-disasters. This study focused on moving particle semi-implicit(MPS) method, which is a Lagrangian gridless particle method, and investigated its performance and stability to simulate large deformation of geomaterials. A calculation method was developed using geomaterials modeled as Bingham fluids to improve the original MPS method and enhance its stability. Two numerical tests showed that results from the improved MPS method was in good agreement with the theoretical value.Furthermore, numerical simulations were calibrated by laboratory experiments. It showed that the simulation results matched well with the experimentally observed free-surface configurations for flowing sand. In addition, the model could generally predict the time-history of the impact force. The MPS method could be a useful tool to evaluate large deformation of geomaterials.

Controlled buckling of thin film on elastomeric substrate in large deformation

Electronic systems with large stretchability have many applications.A precisely controlled buckling strategy to increase the stretchability has been demonstrated by combining lithographically patterned surface bonding chemistry and a buckling process.The buckled geometry was assumed to have a sinusoidal form,which may result in errors to determine the strains in the film.A theoretical model is presented in this letter to study the mechanics of this type of thin film/substrate system by discarding the assumption of sinusoidal buckling geometry.It is shown that the previous model overestimates the deflection and curvature in the thin film.The results from the model agree well with finite element simulations and therefore provide design guidelines in many applications ranging from stretchable electronics to micro/nano scale surface patterning and precision metrology.

UNSYMMETRICAL LARGE DEFORMATION PROBLEM OF ORTHOTROPIC PLATES

Based upon the theory of ardsotropic plates, the unsymmetrical large deformation equations of orthotropic circular plates were derived. By using Fourier series, the partial differential equations of this problem can be transformed into sets of nonlinear differential equations . And the procedure to solve the problem using the iterative method is given .

Three dimensional large deformation analysis of phase transformation in shape memory alloys

Shape memory alloys（SMAs）have been explored as smart materials and used as dampers,actuator elements,and smart sensors.An important character of SMAs is its ability to recover all of its large deformations in mechanical loading-unloading cycles without showing permanent deformation.This paper presents a stress-induced phenomenological constitutive equation for SMAs,which can be used to describe the superelastic hysteresis loops and phase transformation between Martensite and Austenite.The Martensite fraction of SMAs is assumed to be dependent on deviatoric stress tensor.Therefore,phase transformation of SMAs is volume preserving during the phase transformation.The model is implemented in large deformation finite element code and cast in the updated Lagrangian scheme.In order to use the Cauchy stress and the linear strain in constitutive laws,a frame indifferent stress objective rate has to be used.In this paper,the Jaumann stress rate is used.Results of the numerical experiments conducted in this study show that the superelastic hysteresis loops arising with the phase transformation can be effectively captured.

EXACT SOLUTION OF LARGE DEFORMATION BASIC EQUATIONS OF CIRCULAR MEMBRANE UNDER CENTRAL FORCE

Exact solution of the nonlinear boundary value problem for the basic equation and boundary condition of circular membrane under central force was obtained by using new simple methods. The existence and uniqueness of the solution were discussed by using of modern immovable point theorems. Although specific problem is treated, the basic principles of the methods can be applied to a considerable variety of nonlinear problems.

Differentiai-algebraic approach to large deformation analysis of frame structures subjected to dynamic loads

A nonlinear mathematical model for the analysis of large deformation of frame structures with discontinuity conditions and initial displacements, subject to dynamic loads is formulated with arc-coordinates. The differential quadrature element method （DQEM） is then applied to discretize the nonlinear mathematical model in the spatial domain, An effective method is presented to deal with discontinuity conditions of multivariables in the application of DQEM. A set of DQEM discretization equations are obtained, which are a set of nonlinear differential-algebraic equations with singularity in the time domain. This paper also presents a method to solve nonlinear differential-algebra equations. As application, static and dynamical analyses of large deformation of frames and combined frame structures, subjected to concentrated and distributed forces, are presented. The obtained results are compared with those in the literatures. Numerical results show that the proposed method is general, and effective in dealing with disconti- nuity conditions of multi-variables and solving differential-algebraic equations. It requires only a small number of nodes and has low computation complexity with high precision and a good convergence property.