Incremental Displacement Research Articles

Calculation of the strength of water management facilities for the sustainable development of rural areas

The physical relations are presented at the loading step of a bulk body in two variants. In the first version, the theory of plastic flow is used. In the second variant, to determine the increments of plastic deformations, a hypothesis is proposed about the proportionality of the increments of plastic deformations to the components of the deviator of stress increments, which made it more correct and easier to obtain the defining equations at the loading step. Variants of physically nonlinear defining equations in the calculation of three-dimensional elements of water management objects are implemented in the developed tetrahedral finite element with nodal unknowns in the form of displacement increments and stress increments.

Three-dimensional thermo-electro-elastic field in one-dimensional hexagonal piezoelectric quasi-crystal weakened by an elliptical crack

In this paper, an analytical solution is developed for the problem of an infinite 1D hexagonal piezoelectric quasi-crystal medium weakened by an elliptical crack and subjected to mixed loads on the crack surfaces. The mixed loads comprise the phonon pressure, phason pressure, electric displacement, and temperature increment, and the crack surfaces can be electrically permeable or impermeable. Based on a general solution, combined with the generalized potential theory, the steady-state 3D thermo-electro-elastic field variables in the quasi-crystal are obtained in terms of elliptic integral functions and elementary functions. Several important physical quantities on the cracked plane, such as the generalized crack surface displacements, normal stresses, and stress intensity factors, are derived in closed forms. An illustrative numerical calculation verifies the presented analytical solution and shows the distribution of the 3D thermo-electro-elastic field. It is indicated that the influence of the phason field on the result is pronounced, especially for the electric field variables, and the electric permeability of crack surfaces has a significant effect on the electric displacement intensity factor at the crack tip.

Volumetric and shear strain localization throughout triaxial compression experiments on rocks

Deformation localization is a widely observed, but rarely quantified process in the crust. Recent observations suggest that the localization of seismicity and fracture networks can help identify the approach to catastrophic failure. Here, we quantify the localization processes of the volumetric and deviatoric strain components in twelve triaxial compression experiments imaged with X-ray tomography. We capture three-dimensional images of the rock cores during triaxial compressing toward failure, and then calculate the local strain components using digital volume correlation. The divergence and curl of the incremental displacement vector field provide the volumetric and deviatoric components of the strain field. We quantify localization using the proportion of the rock occupied by high magnitudes of the volumetric and deviatoric strains, and the Gini coefficient of these high magnitude strains, which measures the deviation from a uniform process. We find that the vast majority, but not all, of the experiments experience strain localization toward failure. The rocks typically experience their maximum degree of strain localization not immediately preceding failure, but on average at 90% of the failure stress. The volumetric strain tends to localize more than the deviatoric strain. These observations support using the localization of the volumetric strain, along with the deviatoric strain, to identify the evolution of the precursory phase preceding earthquakes.

Mitigation of torsional responses in asymmetric base-isolated structures using an optimal distribution of isolators in base story

The present research proposed an optimal design procedure of isolators in the base story of the asymmetric base-isolated structures to mitigate torsional responses. Instead of the distribution of isolators in the base story proportional to the load-bearing surface (case A), two optimal distributions of isolators in the base story, cases B and C, are proposed for this purpose. Case B gives an optimal distribution of isolators in the base story considering the arithmetic mean of the optimal horizontal effective stiffness of isolators for considered earthquakes and case C represents a weighted average of them according to the peak ground acceleration (PGA) of the considered earthquakes. A three-story reinforced concrete structure is adopted for numerical studies. Different eccentricities, e = 10, 20, 30%, in three directions are considered in the structural models. Nonlinear time-history analyses of the structure are carried out using OpenSees software. A particle swarm optimization (PSO) algorithm is utilized to find the optimal distribution of the isolators at the base story in such a way that the maximum torsion of floors is minimized. The simulation results show that case B, in comparison with those given for case A, results in a significant reduction in the maximum torsion of floors, especially in small eccentricities, at the cost of an increase in the maximum floor displacement responses. For most eccentricities, case C significantly reduces the maximum torsion of floors, while the increment of maximum floor displacement in the case has not exceeded 10%. Hence, the proposed approach in case C performs better than case B in the mitigation of torsional responses of asymmetric base-isolated structures. It is also found that by increasing the eccentricities of floors, the reduction average of the maximum torsion of floors is reduced.

Uniportal Endoscopic Interlaminar Decompression in Lumbar Spinal Stenosis: A Comprehensive Review.

From the 1990s, there has been growth in the literature demonstrating the feasibility of minimally invasive approaches for treating variety lumbar spinal disorders. There is still much work to be done in overcoming the technical challenges and explicate relative advantages of endoscopic techniques in lumbar spine surgery. In this comprehensive literature review, we discuss the history, indications, contraindications, surgical techniques, learning curves, technical tips, adverse events, and examine peer-reviewed studies addressing uniportal endoscopic interlaminar decompression in lumbar spinal surgery. This literature review was conducted with keywords "endoscopic," "minimally invasive," "uniportal endoscopic decompression," "interlaminar decompression," and "lumbar spinal surgery" using PubMed, Embase, ClinicalKey, and Google Scholar. Review of 423 patients who underwent uniportal endoscopic interlaminar lumbar decompression showed satisfying results with 82% of patients no longer having leg pain, and 13% of patients having only occasional pain, with no significant operation-related deterioration in leg or back pain. To compare the outcomes between endoscopic and microscopic technique, a comparative review of 192 lumbar lateral recess stenosis patients demonstrated the uniportal endoscopic group had 29% shorter operation duration, 1.2% fewer perioperative complications, and significantly reduced postoperative pain (visual analog scale) over 5 days, and reduced use of pain medications. Multiple retrospective studies echoed the outcomes of endoscopic decompression surgery, showed shorter hospitalization time, lower mean dural expansion, lower increment of horizontal displacement measured, and less elevated levels of postoperative serum CPK (creatine phosphokinase) and CRP (c-reactive protein). Lastly, a systematic review and meta-analysis that enrolled 994 patients found that patients who received the full-endoscopic decompression technique showed statistically lower levels of back pain and leg pain and a 40% lower chance of having complications compared with those receiving microscopic decompression in lumbar stenosis. Based on our literature review, there are multiple positive outcomes with endoscopic interlaminar lumbar decompression, which reduces operation duration, perioperative complications, and better postoperative outcomes. However, the technical challenge highlights the importance of further training and innovation in this rapidly evolving field.

Social and urban transformations of the surroundings of Street Markets located in the Historic hub of Cuenca. “9 de Octubre” and “10 de Agosto” Markets

Street markets are public facilities that link commercial activities and cultural exchange, which interact with the urban fabric that they are a part of. Their historical and symbolic values ​​make them vulnerable to transformations that rethink the urban structure, as happens in the immediate surroundings of the “9 de Octubre” and “10 de Agosto” street markets, located in the historic hub of the city of Cuenca, Ecuador, where processes of gentrification, touristification, and commercial gentrification have taken place. In this context, the proposal here is to analyze the urban and social transformations of the last 50 years, using a mixed methodology with an exploratory approach, through observation, surveys, and interviews. In both case studies, the results showed that with the operation of these street markets, commercial activity increased in the respective areas which, together with other associated issues (insecurity, unhealthy conditions, informal trade), are the main triggers for the incremental displacement of the population.

Thermoelastic diffusion phase-lag model for a layer with internal heat and mass sources

This paper analyses a problem of unsteady bulk thermoelastic diffusion perturbations propagation in a multi-component layer. The local equilibrium model describes one-dimensional physical processes in the continuum. It includes the coupled equations of elastic medium motion, heat transfer and mass transfer with cross-diffusion effects. The model also considers phase-lag effects in a continuum with internal heat and mass sources. The unknown functions of displacement, temperature and concentration increments are investigated in the Green's functions and the boundary conditions integral convolution form. We use the integral Laplace transform to time and the Fourier expansion into series by a spatial coordinate to find Green's functions. It allows us to reduce the problem to a system of linear algebraic equations. The Fourier series coefficients originals are found using known theorems and operational calculus tables. The numerical algorithms used is minimised, and Green's functions are analytically found. Calculation examples are represented and analysed.

A Study of the Effects of Geosynthetic Reinforced Soil and Reinforcement Length on GRS Bridge Abutment

The geosynthetic reinforced soil (GRS) bridge abutment with a staged-construction full height rigid (FHR) facing and an integral bridge (IB) system was developed in Japan in the 2000s. This technology offers several advantages, especially concerning the deformation behavior of the GRS-IB abutment. In this study, the effects of GRS in the bridge abutment with FHR facing and the effects of geosynthetics reinforcement length on the deformation behavior of the GRS–IB are presented. The numerical models are analyzed using the finite element method (FEM) in Plaxis 2D program. The results showed that the GRS–IB model exhibited the least lateral displacements at the wall facing compared to those of the IB model without geosynthetics reinforcement. The geosynthetics reinforcement in the bridge abutment with FHR facing has reduced the vertical displacement increments by 4.7 times and 1.3 times (maximum) after the applied general traffic loads and railway loads, respectively. In addition, the numerical results showed that the increase in the length-to-height (L/H) ratio of reinforcement from 0.3H to 1.1H decreases the maximum lateral displacements by 29% and the maximum vertical displacements by 3% at the wall facing by the end of construction. The effect of the reinforcement length on the wall vertical displacements is minimal compared to the effect on the wall lateral displacements.

Size effects on the characteristics of fracture process zone of plain concrete under three-point bending

This paper studies the size effects on the characteristics of fracture process zone (FPZ) of plain concrete, including its physical features and softening behavior. Three-point bending tests were performed on pre-notched beams with similar geometry and different dimensions. Electronic speckle pattern interferometry (ESPI) technique was employed to monitor the crack evolution and full-field deformation of the beams. The development of FPZ was evaluated qualitatively based on the strain fields and quantitatively based on the displacement fields obtained by the ESPI technique. By adopting the incremental displacement collocation method, the tension softening curves (TSCs) of specimens with different sizes were estimated and approximated as bilinear curves. The features identified from the TSCs were correlated to the physical features in the development of FPZ. Finally, an empirical tension softening model and corresponding size-independent parameters were obtained based on the estimated TSCs of different sizes specimens.

Displacements, Strains, and Shear Bands in Deep and Shallow Penetration Processes

When penetrometers or probes are pushed into sand, complex displacement fields, strain fields, and shear band patterns develop. Deep and shallow penetration processes in sands generate substantially different patterns. This paper reports the results of penetration experiments performed in dense air-pluviated sand samples prepared in a half-cylindrical calibration chamber equipped with observation windows that allow the collection of images of the sand during penetration. Both a cone penetrometer (diameter d=38 mm) and a model footing (width B=90 mm) are used in the penetration experiments. Incremental displacement and strain fields in the soil domain are obtained by analysis of the collected images using digital image correlation (DIC) and continuum mechanics. The zero-extension line concept is used to study shear strain localization, and a method is proposed to automatically obtain the orientation of shear band patterns from the incremental strain fields. For the model footing, the strain fields are found to localize not only near the footing but also away from it, depending on the level of penetration. The shear bands develop in a traditional wedge shape below the model footing and in a fan shape on either side of it. In contrast, for the cone penetrometer, the strain fields localize more intensely near the penetrometer tip. The shear bands develop along the inclined face and near the shoulder of the penetrometer.

Investigating the influence of block rotation and shape on the impact process

A block impact model based on the elasto-viscoplastic macro element approach is developed for regular base prismatic blocks. This model upgrades a previously conceived model for spherical boulders introducing (i) a rotational degree of freedom; (ii) a moment-rotation relationship; (iii) a toppling mechanism. The model can improve rockfall simulations by considering block geometry and the exchange between translational and rotational energies. Model parameters were calibrated by using laboratory tests on vertical impacts. Parametric analyses were carried out to investigate for both vertical and inclined impacts, the effects of block shape and orientation. The influence of these factors on the impact force, the maximum penetration depth as well as the exchange between translational and rotational energies is discussed. A comparison with the available results for small and large scale laboratory tests shows model capabilities and put in evidence the “nonlinear” relationship between maximum acceleration (or equivalently the maximum contact force) and impact translational velocity. For vertical impacts the trend of the maximum penetration depth is a function of the block shape. Prismatic blocks can experience larger values of maximum penetration than spherical blocks characterized by coincident masses and kinetic energies. In case of bouncing of a prismatic block the increment of normal maximum displacement with respect to spherical blocks ranges from about 66% for triangular base prisms to 132% for hexagonal base blocks. In case of no bouncing, the increments range from about 82% for triangular blocks to −32% for hexagonal blocks. Maximum normal forces also depend on block shape and orientation. In case of a vertex impact with no bouncing, triangular blocks show a decrement in the maximum force of about 43% with respect to the spherical block. The increment of initial block angular velocity generates a reduction in both maximum penetration depths and impact forces.

A Comparison of Three Measurement Models for the Wheel-Mounted MEMS IMU-Based Dead Reckoning System

A self-contained autonomous dead reckoning (DR) system is desired to complement the Global Navigation Satellite System (GNSS) for land vehicles, for which the odometer-aided inertial navigation system (ODO/INS) is a classical solution. In this study, we use a wheel-mounted MEMS IMU (Wheel-IMU) to substitute the odometer, and further, investigate three types of measurement models, including the velocity measurement, displacement increment measurement, and contact point zero-velocity measurement, in the Wheel-IMU based DR system. The measurement produced by the Wheel-IMU along with the non-holonomic constraint (NHC) are fused with INS through an error-state extended Kalman filter (EKF). Theoretical discussion and field tests illustrate the feasibility and equivalence of the three measurements in terms of the overall DR performance. The maximum horizontal position drifts are all less than 2% of the total travelled distance. Additionally, the displacement increment measurement model is less sensitive to the lever arm error between the Wheel-IMU and the wheel center.

Impact protection of offshore structures via high specific stiffness sandwich braces with a multistable transition mechanism

ABSTRACT Offshore structures are impacted by environmental loads, and the low damping properties of metal structures make them prone to lasting vibrations. A sandwich metal brace containing an composite column with a multistable transition mechanism, which exhibits a high specific stiffness and enhanced damping, is designed. Performing a hybrid analysis of sandwich lamination and multi-stable buckling and noted: the sandwich structure conducts the effective cross section of bending stiffness of the composite column, which control critical buckling load; the eccentric end caps conduct the loading axis of the composite column, which controls the displacement increment in the postbuckling. So, the force-displacement hysteretic relation of the composite column can be effectually adjusted by the appropriate physical parameters of the asymmetric composite structure of the novel sandwich brace. The novel braces are utilized to stiffen a offshore structure, which effectively mitigates the slamming response in the finite element simulation.

Experimental investigation on the concrete fracture process zone using electronic speckle pattern interferometry

AbstractIn order to advance the understanding of fracture failure mechanisms in concrete, a series of three‐point bend tests of pre‐notched specimens were conducted to study the characteristics of the fracture process zone. Electronic speckle pattern interferometry (ESPI) was used to determine the location and size of the cracks. The experimental results have shown that crack in the pre‐notched concrete beams will initiate when the load increases to 40% of the peak load (Pmax) and expands unstably after reaching the peak load. When the load drops to about 25% Pmax in the load drop section, a complete fracture process zone (FPZ) was developed, and the corresponding crack tip opening displacement is about 7.1 times to the critical crack tip opening displacement. The analysis of surface strain of concrete specimen showed that microcracks will initiate when the surface tensile strain of concrete reaches about 2 × 10−4; when the surface tensile strain value of concrete reaches 4 × 10−2, the FPZ will move forward; the length of the FPZ of concrete essentially remains the same in the entire fracture process, which is about 71% of the ligament height. The analysis of experimental data also shows that the size of the FPZ is not significantly affected by the cubic compressive strength of concrete. In addition, the tension‐softening curves of the specimens were finally determined by using the incremental displacement collocation method, and it is concluded that the critical width of the FPZ is related to the cubic compressive strength of the concrete.

Numerical Simulation of New Support Structure for High In-situ Stress Tunnel of Sichuan–Tibet Railway

Existing support technology can easily cause the shield machine to jam. A novel ductile support structure is proposed for large deformation tunnels in soft rock along the whole Sichuan–Tibet railway on the basis of the concept of consuming energy of ductile multilevel yielding support. The design of the support structure is to ensure the safety of the shield machine through the large deformation section of soft rock as quickly as possible. In-situ stress data obtained by hydraulic fracturing measurement method were used as boundary conditions of models. The support structure deformation of front shield tunnelling machine and long-term deformation of corrugated steel primary support, steel waist beam and reinforced concrete secondary lining support system were simulated and analysed on FLAC3D software. The variation of the new support structure under the large deformation of soft rock was predicted. Results show that the force path of ductile multilevel yielding support structure is clear. After the excavation of the tunnel and before the application of the concrete lining support, displacement increment of the primary support structure is large. The latter gradually slows down with time, but it still shows an increasing trend. In terms of total displacement distribution, the displacement in the Z direction is obviously larger than that in the X direction, which is consistent with the actual tunnel deformation characteristics. When the tunnel is in operation for 2, 10, 50 and 100 years, stress concentration is found in the arch foot of the assembled supporting system. This condition is mainly manifested as compressive stress after 10 years and tensile stress between 10 and 100 years.

Modular implementation framework of partitioned path-following strategies: Formulation, algorithms and application to the finite element software Cast3M

Damage, cracking, and strain localization mechanisms often lead to unstable structural responses characterized by snap-backs (i.e., force and displacement decrease simultaneously). Standard nonlinear Newton-based solution algorithms with displacement/force control cannot capture the equilibrium curve in its entirety. This can be overcome using path-following formulations. A general (i.e., valid for any finite element code) implementation framework can be designed and applied to the Cast3M software by collecting the essential concepts and the formalism of partitioned path-following arc-length algorithms. Thanks to these developments, Cast3M is now capable of processing path-following equations without any major modifications. Three path-following constraints were selected to demonstrate the applicability of this framework: a first one on the combination of the displacement increment at a given set of nodes, a second one on the maximum strain increment over the computational domain, and a third one on the maximum elastic predictor of the damage/plastic criterion function over the computational domain. Two- and three-dimensional strain localization simulations show that the proposed framework behaves in a stable and convergent manner, even when multiple severe snap-back instabilities are present. Users of Cast3M shall find the proposed study helpful in that it allows them to focus on developing new path-following equations for the software. Cast3M is developed by the French Alternative Energies and Atomic Energy Commission (CEA) and freely available for research purposes. The developments discussed in this paper have been made available to the user/developer community along with Cast3M 2021 (release date: June 2021).

Inexact Newton Woodbury method for efficient structural nonlinear analysis

Nonlinear analysis has become an indispensable means for structural performance evaluation, but is still an expensive process especially for large and complex structures. Although the computer technology has largely improve the performance of nonlinear analysis, more efficient and accurate methods still attract the attention of the researchers. The Woodbury nonlinear method which uses the Woodbury formula to solve the incremental displacement response is an efficient kind of method for local nonlinear analysis, but it is no longer applicable for problems with large part of nonlinearity. Although some approximate methods have been proposed to improve the solution of linear equations in Woodbury nonlinear method, the induced error cannot be effectively controlled which leads to decreasing the convergence rate of the iterative computation and offsetting the improved computational efficiency. To address this problem, this paper proposes the Inexact Newton Woodbury (INW) method for efficient nonlinear analysis, which comprehensively considers the efficiency of both the solution of the linear equations and iterative computation. In terms of the linear equations, the improved Woodbury method is presented, where the approximation method is combined with the Woodbury formula, considerably enhancing the solution efficiency of the linear equations and largely extending the application range of the Woodbury formula. Moreover, to ensure the convergence rate which is another important influence factor of the overall nonlinear analysis efficiency, the inexact Newton condition with a new proposed forcing term applicable for the INW method is employed to make the iterative computation with superlinear convergence rate. Then, the time complexity analysis is conducted to make a comprehensive evaluation of the proposed INW method and the traditional Finite Element Method (FEM) from the aspects of the linear equations solution and iterative computation. The results show that the INW method is more efficient than the FEM especially for problems with large part of nonlinearity. Finally, a simulation example is presented to validate the efficiency and accuracy of the INW method. The results demonstrate that the INW method has higher efficiency under comparable accuracy with the Woodbury nonlinear method so that it has significantly potential for large part of nonlinearity problems. CE Database Subject Headings: Engineering structures; finite element method; material nonlinearity; time complexity

Numerical Analyses on the Behavior of Geosynthetic-Reinforced Soil: Integral Bridge and Integrated Bridge System

Geosynthetic-reinforced soil (GRS) technology has been used worldwide since the 1970s. An extension to its development is the application as a bridge abutment, which was initially developed by the Federal Highway Administration (FHWA) in the United States, called the GRS—integrated bridge system (GRS-IBS). Now, there are several variations of this technology, which includes the GRS Integral Bridge (GRS-IB) developed in Japan in the 2000s. In this study, the GRS-IB and GRS-IBS are examined. The former uses a GRS bridge abutment with a staged-construction full height rigid (FHR) facing integrated to a continuous girder on top of the FHR facings. The latter uses a block-faced GRS bridge abutment that supports the girders without bearings. In addition, a conventional integral bridge (IB) is considered for comparison. The numerical analyses of the three bridges using Plaxis 2D under static and dynamic loadings are presented. The results showed that the GRS-IB exhibited the least lateral displacement (almost zero) at wall facing and vertical displacements increments at the top of the abutment compared to those of the GRS-IBS and IB. The presence of the reinforcements (GRS-IB) reduced the vertical displacement increments by 4.7 and 1.3 times (max) compared to IB after the applied general traffic and railway loads, respectively. In addition, the numerical results revealed that the GRS-IB showed the least displacement curves in response to the dynamic load. Generally, the results revealed that the GRS-IB performed ahead of both the GRS-IBS and IB considering the internal and external behavior under static and dynamic loading.

Formation and evolution of fracture spacing on various geometric surfaces in layered materials

Fracture spacing as a widespread phenomenon in nature shows similar patterns on various geometric surfaces. To explore the similarities and differences between various geometric surfaces in the process of fracture spacing formation, numerical simulations are conducted on bi-layered three-dimensional models of three various geometric surfaces, including slab surface, cylindrical surface, and spherical surface by the finite element method (FEM). The fractures develop under a quasi-static loading condition with constant displacement increments. The progressive failure process from fracture initiation to saturation is researched, and the material heterogeneity is introduced by using a probability distribution, which acts as the main reason for failures generating randomly inception. An intuitive explanation is also provided for the phenomenon of fracture saturation. Then, as the loading condition varies, fracture patterns in both slab surface models and cylindrical surface models show a transition from parallel fractures, step-like fractures to regular polygonal fractures. However, in spherical surface models, only uniform polygonal fractures emerge under the condition of radial expansion. Furthermore, through quantitative analysis by statistical means, we find that, except for the fractured layer thickness, curvature also has a significant impact on the crack density.

Consolidation deformation of hydrate-bearing sediments: A pore-scale computed tomography investigation

Consolidation deformation is prevalent in hydrate-bearing sediments due to oceanic currents, the erection of jack-up drilling rig platforms, depressurization exploitation, etc. However, the microstructural behavior of hydrate-bearing sediment during consolidation remains unclear because of experimental challenges. Herein, using a novel microfocus X-ray CT-based triaxial testing apparatus, we present a series of results to reveal the microstructural evolution of hydrate-bearing sediment using the pixel-tracking technique at the submillimeter level. Initially, a stepped cone-shaped incremental displacement distribution with a relatively large deformation was observed, a rapid decline in the total number and radii of pores was noted, and the hydrate-sand interfacial area was greatly enlarged. Later, only some scattered large incremental displacement zones were found, the decline in the total number and radii of pores slowed, and the increase in the hydrate-sand interfacial area also slowed. The deformation pattern inside the hydrate-bearing sediment presented a strong relationship with the hydrate saturation; however, no obvious hydrate crushing occurred within 3 MPa of effective confining pressure, either visually or quantitatively. The consolidation could lead to a more complex pore system and lower coordination number between the pore and the throat, which led to a decrease in absolute permeability.