Cross-sectional Deformation Research Articles

Deformations and damages of tunnels subjected to strike-slip faulting: Effects of tectonic stress and cross-sectional shape

Deep-buried tunnels are vulnerable to strike-slip faulting, the responses of which are complicated. However, the effects of tectonic stress and cross-sectional shape on behaviors of tunnels in strike-slip faults have not been detailly investigated. This study performs numerical modeling to study the deformations and damages of tunnels subjected to strike-slip faulting, focusing on the effects of tectonic stress and cross-sectional shape. A three-dimensional numerical model is applied, which is validated by the test from the previous study. Different lateral stress coefficients (from 0.5 to 3.0) and cross-sectional shapes of tunnels (circular shape, horseshoe shape, and egg shape) are modeled. The results show that tectonic stress and cross-sectional shape have a great influence on tunnel responses during strike-slip faulting. The failure mode of the tunnel is highly dependent on the tectonic stress. The tensile damage controls in low tectonic stress conditions, while compressive damage domains in high tectonic stress conditions. The tensile damage initials at the arch waist in the vicinities of fault planes, while the compressive damage mainly occurs at the tunnel vault and bottom in the whole fracture zone. Besides, tectonic stress has apparent effects on the transverse displacement of the tunnel axis and the compressive damage range. The H-shaped tunnel behaves the worst, experiencing the largest cross-sectional deformation, the largest compressive damage range, and the smallest required fault deformation for compressive damage.

Fiber-level modeling of 3D braided preforms using virtual braiding method

High fidelity geometry models of the preforms are essential in mechanical property analysis for composite materials. The paper presents a virtual braiding method to generate digital material twins of 3D braided preforms. The four-step 3D braiding process is simulated based on the concept of virtual fiber and according to the rule of yarn movement. Fiber-level models of the preform are constructed which display the micro-scale architectures explicitly, including compressive deformations of yarn cross-sections and variations of yarn paths. The Micro-CT test is employed to investigate the internal fiber structures of 3D braided preform and quantitatively verify the accuracy of the proposed modeling method. Influence of the braiding parameters, such as yarn tension and arrangement angle in the initial state on geometric parameters of the preform is then investigated.

Dynamic buckling response of buried X70 steel pipe with bolted flange connection under two-charge explosion loads

It is of great significance to investigate the dynamic response of pipes under blasting loads for the operation, assessment, and repair of pipes. However, there are few studies available on the dynamic buckling response of pipes under multiple explosion loads. In the present study, pipe-soil coupling 3-D models are established to investigate the dynamic buckling response of X70 steel pipe with bolted flange connection (BFC) under two-charge explosion loads (Charge A lied on the ground surface and Charge B lied in the soil). The main influencing factors are also discussed, including explosion mode, internal pressure, interval time, mass ratio of charges, and diameter-to-thickness ratio (D/t ratio). When Charges A and B were exploded simultaneously, it is found that the non-pressurized X70 pipe produced more significant cross-sectional deformation than in one-point explosion (Charge A or B). Increasing D/t ratio is advantageous for the anti-explosion of the pipe with BFC. Suitable internal pressure can effectively prevent the buckling deformation of the pipe. Compared with the common straight pipe, BFC system can effectively decrease the local buckling deformation and improve the anti-explosion ability of the pipe due to its higher local stiffness and energy absorption.

Simulating the hysteretic behaviour of thin-walled H-Section steel members using the geometrically exact beam theory

Based on Gonçalves's geometrically exact beam theory considering cross-section deformation, the warping and distortional deformation of thin-walled members are described in this paper by means of a combination of section deformation modes. By integrating with the J2 elastic‒plasticity theory for the steel, a numerical model is established for the hysteretic behaviour of thin-walled steel members. Four classes of H-section members are selected on account of the design codes, and the influence of section warping and distortion deformation modes on the calculation of the hysteretic behaviour of components with different section types is analysed. The crucial aspect lies in the bending hysteresis behaviour around the strong and weak axes of the cross-section for H-beam steel members subjected to typical thin-walled members with relatively large widths and thicknesses. Test results on the hysteretic behaviour of H-section steel members are compared with those calculated from the proposed model in terms of the hysteric behaviour of components, strength degradation, energy-dissipating capacity, etc. These findings validate the correctness and feasibility of the established non-linear analysis model for thin-walled members.

Research Overview on Rectangular Tube Cross-Section Deformation in Rotary-Draw Bending Process

Rectangular tube bending process forming quality is not only affected by the tube material but also geometric dimensions will also be affected by bending mold and related process parameters. Cross-section deformation produced by the tube during the forming process becomes a major constraint to heightening the quality of the tube. The research work and process of cross-section deformation in the rotary-draw bending process (RDBP) of rectangular tubes in theory analysis, experiment research, and finite-element (FE) simulation in recent years is reviewed in this paper. The development trend of research in this field is also proposed.

A novel numerical framework to simulate mechanical response and damage characteristics of mountain tunnels under faulting

This paper presents a novel numerical framework that can simulate the mechanical response and damage characteristics of mountain tunnels under faulting more precisely and efficiently. Both the submodeling and two-stage models are adopted in the framework. The submodeling technique is used to obtain a precise simulation of tunnel-fault interaction while ensuring computational efficiency. The two-stage models can acquire accurate initial stress of the tunnel lining and simulate the tunnel-rock interaction during fault movement, which can also achieve the transition from static to dynamic analysis. The computational efficiency can be improved by about 73 % via the proposed numerical framework compared to the conventional numerical analysis when keeping the same mesh sizes. Moreover, overall lining damage indices and cross-sectional ovalization are introduced to quantitatively evaluate the respective damage and deformation of the tunnel lining cross-section, and damage level classifications for tunnel lining under faulting are established. Parametric sensitivity analyses are performed to investigate key factors affecting the mechanical damage behavior of mountain tunnels under strike-slip faulting, including fault dislocation, fault zone width, and the tunnel-fault intersection angle. The increasing fault dislocation causes larger tunnel-rock interaction around the fault plane, making the damage and deformation of tunnel lining around the fault plane more severe. The fault zone width has a significant impact on the damage and deformation range of tunnel lining. The tunnel-fault intersection angle contributes great influence on the magnitude and range of tunnel lining damage and deformation. The tunnel lining would suffer relatively severe damage and deformation when the two fault blocks move away from each other along the tunnel axial.

Experimental investigation of seismic performance of segmental tunnel with secondary lining under strong earthquake

To assess the seismic performance of large-diameter tunnels in soil ground with and without secondary lining, large scale shaking table tests with geometrical ratio of 1:15 were conducted. The model tunnels were grouped as a tunnel only with segmental linings (Single lining), a tunnel liner with additional semi-ring secondary lining (Semi-ring), and a tunnel with additional full-ring secondary lining (Full-ring). Transverse excitations input from shaking-table were designated as Shanghai artificial accelerogram with magnitudes from 0.3 to 1.0 g. Measurements were made mainly on the time histories of acceleration responses, cross-sectional deformation, extension/closure at longitudinal joints of segmental linings, and earth pressure on external surface, of the model tunnels. Comparison the seismic responses of the tested models gives the effects of secondary lining as: 1) the distribution of acceleration responses on segmental linings is significantly different in the case of single lining model; 2) dynamic normal earth pressure on the external surface of the segmental linings increase along depth, but in different patterns; 3) the constraint effects of semi-ring secondary lining on extension/closure of longitudinal joints are not significant in the upper half of segmental lining. Furthermore, with the increase of earthquake intensity, the constraint effects of full-ring secondary lining on both cross-sectional deformation and extension/closure of longitudinal joints become more remarkable, compared with those of the semi-ring secondary lining.

Dynamic Stability of a Three-Layer Beam – Generalisation of the Sandwich Structure Theory

Abstract The work focuses on the dynamic stability problem of a simply supported three-layer beam subjected to a pulsating axial force. Two analytical models of this beam are developed: one model takes into account the non-linear hypothesis of cross-section deformation, and the other takes into account the standard “broken line” hypothesis. Displacements, strains and stresses for each model are formulated in detail. Based on the Hamilton principle, equations of motion are determined for each of these models. These systems of two differential equations for each model are approximately solved with the consideration of the axial pulsating force, and the fundamental natural frequencies, critical forces and the Mathieu equation are determined. Detailed studies are performed for an exemplary family of beams. The stable and unstable regions are calculated for the three pulsating load cases. The values of fundamental natural frequencies and critical forces of exemplary beams calculated from two models are compared.

Research the Dimensional Accuracy of C45 Steel Ring Forgings Produced by Radial Rolling.

The rolling process of rings is a commonly used method for producing annular forgings. There are two primary types of this process: radial-axial rolling and radial rolling. This article presents the research results regarding the latter, in which obtaining a product with the assumed dimensions constitutes a major problem. In industrial practice, the process parameters are based on the experience of technologists and/or by trial and error. This is why the authors considered it justified to undertake the research aimed at determining the influence of the main process parameters, that is, preform temperature and tool speed, on the shape and dimensions of the cross-section, which determine the internal and external diameters of the rolled ring. The research was based on numerical simulations and experimental studies. The results obtained proved that the higher the feed speed of the main roll, the greater the change in the cross-sectional height during rolling, and the smaller the cross-sectional deformation (the so-called fishtail). Nevertheless, a higher preform temperature reduces the final height of the ring and reduces cross-section deformation. On the basis of the obtained test results, guidelines for the process design were postulated, considering the influence of temperature and speed parameters on the final dimensions of the forging and the dimensions of the preform.

Pure/combined buckling mode calculation of thin-walled members constraining general shell FE models

This paper proposes a technique for decomposing the buckling solution of thin-walled members into pure deformation modes (global, distortional, local, or other), aiming at providing an insight into the buckling behavior of these members. The calculation of critical loads associated with a specific or combined deformation mode is performed constraining general finite element models. A general constraining procedure is presented, in which the critical load of any mode, combining different section deformation modes and different harmonic shape functions in the longitudinal direction, can be determined. Cases where all possible harmonic terms may be automatically considered are also described. Cross-section deformation modes are defined in the context of the constrained finite strip method (base vectors), and the proposed constraining procedure is implemented by means of relationships between degrees of freedom of the finite element mesh in commercial software. Calculation of combined buckling modes inherently makes it possible to quantify the participation of the considered modes, including along specific longitudinal segments of the member. Results from the analysis of a lipped channel member are presented to demonstrate the concepts and, later, the analysis of a member with a more complex cross-section and intermediate boundary conditions along length is detailed. A discussion on the base vectors chosen for the constraining method is presented. Finally, the potential of the proposed method is discussed.

Constraining effect of load frames during full-scale rotor blade fatigue testing

In rotor blade fatigue tests used for the certification process, load frames are used to introduce the loads to the blade. These load frames have a constraining effect on the cross-sectional deformation. This work investigates these constraining effects using a finite element contact analysis on a current-generation commercial rotor blade. Two different load frame variants are considered: a conventional load frame covering most of the cross-section and a reduced load frame covering only the main spar caps. The interaction between blade and load frame is implemented via contact formulations, which allows pretensioning in combination with a flap and a lead-lag load case. Strains on the outer surface of the blade are evaluated and compared to an artificial reference loading. The area of influence of the load application through the load frame, in which the strains deviate significantly due to clamping effects, mostly corresponds to the 0.75 times the chord length assumed for the certification [1]. The strains in the trailing edge are significantly less affected by the reduced load frame variant than by the conventional one, thus potentially making it possible to consider the trailing edge at the position of the load frame as being properly tested for certification purposes.

Impact of shell structure stiffness on aero-structural coupling in wind turbine rotor blades

Wind turbine rotor blades are heavily loaded composite structures that experience a mixture of aerodynamic, inertial, gravitational, and gyroscopic forces during their operation life. Due to the high loads, the cross-sections of the blades are subjected to in-plane and out-of-plane deformations. The out-of-plane deformations are referred to as shear warping while the in-plane deformations are also called blade breathing. Blade breathing depends on the magnitude of the mechanical loads, which are expressed by means of internal forces and moments, and the stiffness of the blade shell.In this work, the relationships between in-plane cross-sectional deformations and internal loads are investigated. For the quantification of the deformation, a reference blade is studied via 3D finite shell element simulations for different loading scenarios. The cross-section of interest is located at the radial position of maximum chord. To compare the shape of the cross-sections in the undeformed and the deformed configurations, a procedure is proposed to relate the positions of nodes associated with the cross-section of interest in both configurations to a joint coordinate system. The shape of the deformed cross-section is then extracted and compared with the undeformed configuration. The comparison is executed for the individual internal forces and moments, namely flapwise and edgewise bending moments, normal force, shear forces, and torsion moment, respectively. The deformation patterns are discussed and it is addressed how these may influence the aerodynamic behavior of the cross-section under consideration.

Experimental Study on Seismic Response of Underground Tunnel–Soil–Piled Structure Interaction Using Shaking Table in Loose Sand

The seismic response of structures can have a significant impact on adjacent structures’ response. Although several numerical studies have been applied in the field of tunnel–soil–pile interaction systems, there is a lack of experimental research specifically focused on the effects of this interaction on tunnel cross-section deformation and the existence of structure on encircling soil response. In this study, shaking table tests were conducted to examine the seismic response of a tunnel and the surrounding soil when an eight-story structure with piles was located in the vicinity of the tunnel. Four series of physical models were analyzed, including free-field soil (S), tunnel–soil (TS), soil-piled structure (SP), and tunnel–soil-piled structure (TSP), under sinusoidal vibration at three frequencies on loose sand. According to the results, the tunnel significantly impacts the surrounding soil response during seismic excitation with reduced acceleration at the tunnel invert and increased acceleration at the tunnel crown. In the TSP model, applied frequency affects the recorded acceleration amplitude at the tunnel invert. Although acceleration amplitude decreases at 3 Hz frequency excitation compared to the free field model, 8 Hz excitation resulted in bigger values in tunnel invert. Displacements are higher at the tunnel crown, indicating tunnel-induced soil deformation and maximum shear strain concentrated near the tunnel crown. The tunnel cross-section exhibited oval shape changes, with higher forces on the tunnel crown in the presence of piles.

On the buckling propagation and its arrest in buried offshore pipeline crossing strike-slip fault

This study focused on buckling propagation and its arrest in buried offshore pipelines crossing strike-slip faults. A buried offshore pipeline with integral arrestors was analyzed using nonlinear vector-form-intrinsic-finite-element-method-based shell elements and modified soil springs. The effects of different external pressures on structural response were investigated. Integral arrestors with different design parameters were tested to prevent flattening and flipping propagation. The results showed seven or five fluctuations in the flattening parameters with alternating orthogonal directions along the pipeline. These fluctuations led to multi-failure modes, including S-shaped and Z-shaped flexures, two local collapses followed by flattening propagations, and a single local collapse followed by flipping propagation. Integral arrestors should be designed specifically to provide sufficient local bending rigidity in the circumferential direction. The arrest mode of flattening propagation is stopping the earliest fluctuations whilst that of flipping propagation is stopping the earliest fluctuations and depressing the downstream reverse ovalities. For the same arrestor thickness, the smallest effective arrestor length to stop flattening propagation was significantly less than that for flipping propagation. The arrest is temporary because of gross deformation of cross-sections at integral arrestors or the downstream pipes, and secondary failure accidents are likely to occur with any external perturbation.

A comprehensive analysis for real-time shape and strain sensing of composite thin-walled structure

This study presents an effective and reliable shape sensing strategy to model the flat cross section deformation of laminated composite thin-walled structure. The proposed strategy is derived by using the customized isogeometric I-beam elements and Murakami zigzag theory (MZT), named IG-MZT(I). Compared to the traditional reconstruction model, the IG-MZT(I) offers numerous advantages for displacement and strain analysis of composite thin-walled structure such as high-order continuity representation, simple mesh refinement, and fewer strain sensors. Initially, the theoretical framework of composite I-beam element based on the MZT deformation theory is presented. Then, the isogeometric analysis is introduced to approximate the displacement field, and the order of B-spline basis functions can be determined by the constitutive equations.Furthermore, an intuitive strain conversion model is established for solving the geometric complexities in strain measurements. Finally, utilizing a least-square variational function within IG-MZT(I) enables the establishment of the shape sensing formula. Several numerical analyses and experiment results demonstrate the outstanding accuracy and reliability of the proposed approach for reconstructing composite I-beams.Overall,the present model is simple and independent of the traditional composite reconstruction models that require embedded sensors,making the IG-MZT(I)sufficiently general to analyse the composite structure in service.

Buckling collapse of reinforced thermoplastic pipes (RTPs) with initial imperfections subject to external pressure

In the present study, the collapse behavior of RTPs was analyzed by an experimentally-verified numerical method, in which the eccentricity directions, the combinations of eccentricity and initial ovality are considered. Eigenvalue analysis and Riks analysis were combined to simulate the progressive failure of composites during the collapse, which was conducted by a continuum damage model based on Hashin failure criterion and fracture energy dissipation. The stress analysis showed that the hoop stress of composites is much higher than that of isotropic layers both in the elastic and progressive failure phases. Because of this, thick composites always play important roles in bearing external pressure. Except the experimentally observed O-/U-type collapse modes, the C-type collapse mode was observed and simulated for the first time. They all go through the uniform contraction-collapse-large deformation process, and have the same failure modes of composites. However, different from the O-/U-type collapse modes, the cross-sectional deformation of the C-type collapse is not symmetrical and has a moving maximum-displacement point. The collapse pressure decreases linearly as the increase of the eccentricity and the initial ovality. The effect of eccentricity directions can be concluded as: more dispersed eccentricity distribution makes composites contribute more to the pressure resistance.

Theoretical analysis, finite element modeling and experimental investigation of the impact of friction between tube and bending die on the formability of the tube during the free-bending process

In the free-bending process, the tube undergoes bending and deformation due to the action of a guide mechanism and bending die. The plastic deformation zone of the bent tube is less constrained by the die, and the quality of the formed tube is significantly affected by the friction between the tube and the die. To assess the impact of friction between tube and die on the formability of the bent tube, the theoretical modeling that considers the friction coefficient is conducted. Afterward, the free-bending experiments and finite element simulations are performed using Cr12MoV and ceramic bushing. The theoretical and experimental results are compared with those obtained from finite element simulation under different friction conditions to confirm the validity of finite element simulation. The influence of friction on the arc radius, wall thickness variation, and cross-section deformation of the curved tube is explored and discussed. With the increase of friction coefficient, the arc radius decreases gradually, the wall thickness thickens more obviously, and the cross-sectional distortion becomes more serious. Furthermore, the effect of different bushing materials on the surface quality of aluminum alloy and stainless-steel bent tubes is experimentally investigated. Those findings expand our understanding of the influence of tube-die friction on deformation behavior and it is necessary to first determine the friction condition during the actual free-bending forming process.

Forming method and cross-section deformation of transition section of finned special-shaped tubes in 3D free bending technology

In 3D free-bending technology, the bending forming of the tube consists of the transition section and the stable forming section. However, because of the continuous movement of the bending die and tube in the transition section, the forming mechanism of the tube in the transition zone is relatively complex and still unclear. In addition, due to the complexity of the cross-section deformation of the finned special-shaped tube (FSST), its application in the heat dissipation pipeline of aerospace vehicles is severely hindered. To address the above issues, in this paper, a 3D free-bending forming process method, which can effectively coordinate the movement of FSST and the bending die in the transition section, was proposed. Meanwhile, an analytical model of FSST bending forming was established, which can effectively characterize the elastic-plastic evolution of the FSST cross-section and match the bending radius with the cross-sectional bending moment effectively. Then, the effectiveness of the process method and analytical model was verified by finite element model (FEM), and experiments. Further, FEM and experiments were used to investigate the influence of the process parameters of the transition section on the forming radius and cross-section deformation of FSST after springback. The results from this study show that reasonable coordination of the rotation speed of the bending die and the advancing speed of FSST in the transition zone can improve the forming quality of FSST.

A new algorithm to generate randomly distributed fibers within the fiber bundle and numerical investigation of bundle cross-sectional performances in transverse compression

Transverse compression-induced cross-sectional deformation of parallel fiber bundles usually acts as the fundamental structural mechanism for bundle-based materials. In the present article, a meso-scale insight into the cross-sectional responses of parallel fiber bundle under transverse compression was made. A novel algorithm was proposed to design and model the bundle cross-sectional meso-structure with randomly distributed fibers. The transverse compression induced bundle cross-sectional responses (including cross-sectional perimeter, area and filling factor) were simulated and analyzed based on the finite element method, and were verified experimentally for the bundle with 91 fibers. Results showed that the load began to increase significantly when the perimeter growth rate of the bundle cross-section was larger than 0.8, and the load gradually reached the peak value when the perimeter growth rate was about 1.5. The Mises stress distribution of the bundle gradually neared to the Gaussian distribution when load sharply increased. The results presented in the current paper can provide a novel method to generate randomly distributed fibers and a theoretical guidance for the mechanical properties prediction of bundle-based materials by analyzing the bundle cross-sectional deformation in transverse compression.

Automatic Detection and Association Analysis of Multiple Surface Defects on Shield Subway Tunnels.

The surface defects on a shield subway tunnel can significantly affect the serviceability of the tunnel structure and may compromise operation safety. To effectively detect multiple surface defects, this study uses a tunnel inspection trolley (TIT) based on the mobile laser scanning technique. By conducting an inspection of the shield tunnel on a metro line section, various surface defects are identified with the TIT, including water leakage defects, dislocation, spalling, cross-section deformation, etc. To explore the root causes of the surface defects, association rules between different defects are calculated using an improved Apriori algorithm. The results show that: (i) there are significant differences in different association rules for various surface defects on the shield tunnel; (ii) the average confidence of the association rule "dislocation & spalling → water leakage" is as high as 57.78%, indicating that most of the water leakage defects are caused by dislocation and spalling of the shield tunnel in the sections being inspected; (iii) the weakest rule appears at "water leakage → spalling", with an average confidence of 13%. The association analysis can be used for predicting the critical defects influencing structural reliability and operation safety, such as water leakage, and optimizing the construction and maintenance work for a shield subway tunnel.