Stress-based Method Research Articles

State of the practice on energy-based liquefaction evaluation and research significance

<p>Since the 1964 Niigata and Alaskan earthquakes, which incurred severe liquefaction damage, liquefaction-related design for infrastructures and buildings has been developed exclusively on the principle of force equilibrium. However, the energy concept is increasingly recognized as superior for simplified and robust liquefaction designs because of the uniqueness of energy capacity in soil failures regardless of the differences in earthquake loads. The energy-based liquefaction evaluation method (EBM) has been pursued by many investigators where dissipated energy for liquefaction is focused in place of liquefaction strength defined in the conventional stress-based method (SBM). Furthermore, the EBM enables sound liquefaction-related designs without resorting to sophisticated but highly variable/tricky numerical analyses and contributes as a scale to measure the reliability of those numerical tools. Thus, the EBM, though short of practical use in today's engineering works, should be able to serve as a simplified liquefaction evaluation tool besides the SBM. We reviewed the basic idea as well as the recent developments of the EBM together with the supporting data. We also discussed how to simplify and approximate the energy-based liquefaction behavior to implement robust evaluations in practical problems. The EBM liquefaction evaluation steps were delineated and exemplified by case studies for practicing engineers compared to the SBM.</p>

Liquefaction assessment based on numerical simulations and simplified methods: A deep soil deposit case study in the Greater Lisbon

The accurate estimation of earthquake-induced liquefaction damage requires detailed ground response analysis, which does not generally consider liquefaction. This paper presents a well-documented pilot site where different approaches to estimate surface ground motion were compared. A simplified stress-based method and non-linear dynamic effective stress numerical analyses were used to identify liquefaction. HVSR curves were used to validate the numerical analyses and laboratory test results were employed to calibrate an advanced constitutive model capable of reproducing liquefaction stress-strain behaviour and pore water pressure generation.1D non-linear elastic numerical analysis evidenced high shear strains in weak soil layers where liquefaction may occur. When PM4sand model was used to simulate liquefaction behaviour in sandy layers, 1D and 2D model responses were rather similar, since liquefaction occurs predominantly at a sandy layer that extends across the valley. Therefore, 1D horizontally infinite layers seems to be a good approximation of the 2D response of this valley.

Optimizing Deficit Irrigation Management to Improve Water Productivity of Greenhouse Tomato under Plastic Film Mulching Using the RZ-SHAW Model

Deficit irrigation (DI) is a widely recognized water-saving irrigation method, but it is difficult to precisely quantify optimum DI levels in tomato production. In this study, the Root Zone Water Quality-Simultaneous Heat and Water (RZ-SHAW) model was used to evaluate the potential effects of different DI levels on tomato growth in a drip-irrigated field. Combinations of five DI scenarios were tested in greenhouse field experiments under plastic film mulching according to the percentage of crop evapotranspiration (ET), i.e., ET50, ET75, ET100, ET125, and ET150. The model was calibrated by using the ET100 scenario, and validated with four other scenarios. The simulation results showed that the predictions of tomato growth parameters and soil water were in good agreement with the observed data. The relative root mean square error (RRMSE), the percent bias (PBIAS), index of agreement (IoA) and coefficient of determination (R2) for leaf area index (LAI), plant height and soil volumetric water content (VWC) along the soil layers were <23.5%, within ±16.7%, >0.72 and >0.56, respectively. The relative errors (REs) of simulated biomass and yield were 3.5–8.7% and 7.0–14.0%, respectively. There was a positive correlation between plant water stress factor (PWSF) and DI levels (p < 0.01). The calibrated model was subsequently run with 45 different DI scenarios from ET0 to ET225 to explore optimal DI management for maximizing water productivity (WP) and yield. It was found that the maximum WP and yield occurred in ET95 and ET200, with values of 28.3 kg/(ha·mm) and 7304 kg/ha, respectively. The RZ-SHAW demonstrated its capacity to evaluate the effects of DI management on tomato growth under plastic film mulching. The parameterized model can be used to optimize DI management for improving WP and yield based on the water stress-based method.

A novel atomic J-integral concept beyond conventional fracture mechanics

The J-integral, which is crucial to the nonlinear fracture analysis within the framework of continuum fracture mechanics, fails at the atomic scale due to the atomic discreteness emerging with decreasing size. In this paper, a novel atomic J-integral calculation method is proposed for atomically sharp cracks by developing a new integral scheme to describe the local displacement gradient and stress field for discrete models. The applicability of the atomic J-integral is verified by comparing with traditional FEM and stress-based method, and its path-independency is elucidated by evaluating the geometric nonlinearity at the atomic scale. Furthermore, it is corroborated that the atomic J-integral method is dimension-independent even at the ultra-small scale below the dimensional limit of continuum mechanics.

Evaluation of liquefaction potential by energy-based and stress-based methods and gene expressing programming (case study: Tabriz city)

ABSTRACT Liquefaction in soil layers is a vital factor intensifying earthquake damages.This study compares the numerical evaluation process and the results of two methods based on stress and energy. It is inferred from the calculations that the stress-based method predicts a higher liquefaction potential with a lower safety factor as it promises liquefaction in deeper soil layers. In return, liquefaction tends to occur at a shallower depth with higher intensity in the energy-based method. Through applying the two approaches based on the data collected from different areas around Tabriz, a liquefaction-zoning map is presented. Despite being far from the fault, the central to the western and the southwestern parts of Tabriz has a high liquefaction potential. Eventually, based on the evaluated liquefaction potential using the stated methods and adopting the gene expression programming (GEP) approach, an equation is introduced to estimate the liquefaction potential for the case study. The predictions of the proposed models were consistent with the findings of experimental methods, demonstrating appropriate statistical measures and parametric analysis. It can also be concluded from the results of the parametric analysis, that the parameters of maximum acceleration, earthquake magnitude, and SPT number have more great impact on soil liquefaction.

Stress-controlled shear flow alignment of collagen type I hydrogel systems

Disease research and drug screening platforms require in vitro model systems with cellular cues resembling those of natural tissues. Fibrillar alignment, occurring naturally in extracellular matrices, is one of the crucial attributes in tissue development. Obtaining fiber alignment in 3D, in vitro remains an important challenge due to non-linear material characteristics. Here, we report a cell-compatible, shear stress-based method allowing to obtain 3D homogeneously aligned fibrillar collagen hydrogels. Controlling the shear-stress during gelation results in low strain rates, with negligible effects on the viability of embedded SH-SY5Y cells. Our approach offers reproducibility and tunability through a paradigm shift: The shear-stress initiation moment, being the critical optimization parameter in the process, is related to the modulus of the developing gel, whereas state of the art methods often rely on a predefined time to initiate the alignment procedure. After curing, the induced 3D alignment is maintained after the release of stress, with a linear relation between the total acquired strain and the fiber alignment. This method is generally applicable to 3D fibrillar materials and stress/pressure-controlled setups, making it a valuable addition to the fast-growing field of tissue engineering. Statement of significanceControlling fiber alignment in vitro 3D hydrogels is crucial for developing physiologically relevant model systems. However, it remains challenging due to the non-linear material characteristics of fibrillar hydrogels, limiting the scalability and repeatability.Our approach tackles these challenges by utilizing a stress-controlled rheometer allowing us to monitor structural changes in situ and determine the optimal moment for applying a shear-stress inducing alignment. By careful parameter control, we infer the relationship between time, induced strain, alignment and biocompatibility.This tunable and reproducible method is both scalable and generally applicable to any fibrillar hydrogel, therefore, we believe it is useful for research investigating the link between matrix anisotropy and cell behavior in 3D systems, organ-on-chip technologies and drug research.

The establishment of prediction model for soil liquefaction based on the seismic energy using the neural network

In the development of the prediction model for soil liquefaction, compared to the stress-based method, the energy-based methods proposed and developed in recent years are closer to the essence of soil liquefaction which is about the energy dissipation. Therefore, considering the weak nonlinear relationship found by the previous research, the fuzzy neural network (FNN) and BP neural network (BPNN) were adopted to try to obtain a prediction model which is the most proper to this nonlinear relationship. Firstly, the database including 284 cases obtained from laboratory test was divided into 3 separate groups denoted as training, validation set and testing sets by the ratio of 5:1:1; then, the FNN model and BPNN model were iterated to determine the model parameter by referring to the variation of fitness value and relative error of validation set; at the same time, the optimization algorithm of genetic algorithm (GA) was adopted to BPNN to find the best coefficients; besides, the parameter of \({C}_{c}\) and \({D}_{50}\) was respectively excluded from the database to test their influence degree according to the prediction error; finally, six prediction results of FNN and genetic algorithm BP neural network (GABP) were compared with the previously proposed models. The results showed that the relationship of capacity energy to the influencing parameters could not be fitted as a fully linear relationship; the FNN model can learn the role of \({C}_{c}\) in affecting the capacity energy while the GABP model needs not to take it into account; the FNN and GABP model all fitted a good weakly nonlinear relationship for the capacity energy, and the GABP model is a better prediction model for capacity energy so far.

Crack Initiation Evolution Under Triaxial Loading Conditions

In response to high demands for minerals and in the light of rapid advancement in instrumentation and testing facilities, mines, tunnels, and infrastructures are getting deeper at an annual increasing rate. For instance, Australia’s deepest Gwalia gold mine near Leonora is extending beyond 2 km depth in the hunt for more ore. In Europe, the Gotthard sub-alpine base tunnels exceeding 10 m wide are excavated at depths greater than 2 km. At depth, explosion-like fractures occur which are known as stress spalling, slabbing, or rock bursting due to high-pressure environment, high temperature, and low porosity. Although rockburst and spalling failures have both been observed in the past 50 years and investigated by numerous researchers, this phenomenon is yet mysterious and the physics behind is still not fully understood. Recent researches have suggested that the spalling strength can be related to the crack initiation point. Various methods have therefore been proposed to identify the crack initiation at laboratory scales based on stress-strain response. Limited models are also available based on applied stresses, but only under triaxial conditions. This study aims to compare the volumetric strain method (as a strain-based technique) with the improved Griffith and Hoek-Brown criterion (G-HB) (as a stress-based method) to determine the crack initiation stress threshold under triaxial loading conditions.

A novel approach to modelling the bond characteristics between CFRP fabrics and steel plate joints under quasi-static tensile loads

Carbon fiber-reinforced polymer (CFRP) materials have been effectively used as externally bonded sheets to repair damaged steel structures such as airplanes and ships. In this study, a series of double strap joints with different bonding lengths are considered and examined to experimentally and theoretically assess the effective bond length. Various models exist in the literature which are used to predict the strength of steel and CFRP joints under various loading conditions. Non-linear Lagrange stress method (NLS) which is a novel stress-based method for predicting the failure load values is presented for the first time. This approach is based on 2D and 3D linear elastic finite element analysis. Relying only on two experimental tests, the new approach proposed here can quickly and easily predict the failure load in steel/CFRP samples. In this methodology, it is assumed that the adhesive joint will fail as the normal stress along the adhesive mid-line reaches a predetermined value at a critical distance. In addition, experimental data on steel/CFRP joints gathered from the literature are compared to predictions using the NLS method. It was found that results from the theoretical predictions (NLS) were in good agreement with experimental tests conducted on double strap joints. It was also revealed that the average accuracy of the NLS method is superior to other methods such as cohesive zone model and Hart-Smith. The results revealed that under the best conditions, the NLS model is 5 times more accurate than existing models.

Fourier Integral Transformation Method for Solving Two Dimensional Elasticity Problems in Plane Strain Using Love Stress Functions

The Fourier integral method was used in this work to determine the stress fields in a two dimensional (2D) elastic soil mass of semi-infinite extent subject to line and strip loads of uniform intensity acting on the boundary. The two dimensional plane strain problem was formulated using stress-based method. The Fourier integral was used to transform the biharmonic stress compatibility equation to a fourth order linear ordinary differential equation (ODE) in terms of the stress function. The ODE was solved subject to the boundedness condition to obtain the bounded stress function. Cartesian stress components were obtained using the Love stress functions. Application of the stress boundary conditions for the case of line load of uniform intensity and the cases of uniformly distributed load on a strip of finite width gave the respective unknown constants of the Love stress functions; and hence the complete determination of the Cartesian stress components for the two cases considered. Inversion of the Fourier integral expressions obtained for the normal and shear stresses in the Fourier parameter gave respective expressions for the normal and shear stress fields for line and finite strip loads of finite width in the physical domain variables. The results obtained agreed with the results from previous studies which used displacement based methods.

Electric Stimulation of Astaxanthin Biosynthesis in Haematococcus pluvialis

The green microalga Haematococcus pluvialis accumulates astaxanthin, a potent antioxidant pigment, as a defense mechanism against environmental stresses. In this study, we investigated the technical feasibility of a stress-based method for inducing astaxanthin biosynthesis in H. pluvialis using electric stimulation in a two-chamber bioelectrochemical system. When a cathodic (reduction) current of 3 mA (voltage: 2 V) was applied to H. pluvialis cells for two days, considerable lysis and breakage of algal cells were observed, possibly owing to the formation of excess reactive oxygen species at the cathode. Conversely, in the absence of cell breakage, the application of anodic (oxidation) current effectively stimulated astaxanthin biosynthesis at a voltage range of 2–6 V, whereas the same could not be induced in the untreated control. At an optimal voltage of 4 V (anodic current: 30 mA), the astaxanthin content in the cells electro-treated for 2 h was 36.9% higher than that in untreated cells. Our findings suggest that electric treatment can be used to improve astaxanthin production in H. pluvialis culture if bioelectrochemical parameters, such as electric strength and duration, are regulated properly.

Stress-Based FEM in the Problem of Bending of Euler-Bernoulli and Timoshenko Beams Resting on Elastic Foundation.

The stress-based finite element method is proposed to solve the static bending problem for the Euler–Bernoulli and Timoshenko models of an elastic beam. Two types of elements—with five and six degrees of freedom—are proposed. The elaborated elements reproduce the exact solution in the case of the piece-wise constant distributed loading. The proposed elements do not exhibit the shear locking phenomenon for the Timoshenko model. The influence of an elastic foundation of the Winkler type is also taken into consideration. The foundation response is approximated by the piece-wise constant and piece-wise linear functions in the cases of the five-degrees-of-freedom and six-degrees-of-freedom elements, respectively. An a posteriori estimation of the approximate solution error is found using the hypercircle method with the addition of the standard displacement-based finite element solution.

Bending analysis of five-layer curved functionally graded sandwich panel in magnetic field: closed-form solution

In this paper, an exact closed-form solution for a curved sandwich panel with two piezoelectric layers as actuator and sensor that are inserted in the top and bottom facings is presented. The core is made from functionally graded (FG) material that has heterogeneous power-law distribution through the radial coordinate. It is assumed that the core is subjected to a magnetic field whereas the core is covered by two insulated composite layers. To determine the exact solution, first characteristic equations are derived for different material types in a polar coordinate system, namely, magneto-elastic, elastic, and electro-elastic for the FG, orthotropic, and piezoelectric materials, respectively. The displacement-based method is used instead of the stress-based method to derive a set of closed-form real-valued solutions for both real and complex roots. Based on the elasticity theory, exact solutions for the governing equations are determined layer-by-layer that are considerably more accurate than typical simplified theories. The accuracy of the presented method is compared and validated with the available literature and the finite element simulation. The effects of geometrical and material parameters such as FG index, angular span along with external conditions such as magnetic field, mechanical pressure, and electrical difference are investigated in detail through numerical examples.

Variability effect of strength and geometric parameters on the stability factor of failure surfaces of rock slope by numerical analysis

In loose or highly weathered rock slopes, the circular shear failure mechanism occurs in large scale. Most rock slope stability investigations ignore the influence of geometric parameters, i.e., failure surface entry point distance (le). This study presents failure surface determination based on constant element stress-based method. The failure surfaces and their sliding mechanism are analyzed first by using FLAC3D (Fast Lagrangian Analysis of Continua in three-dimension). A real case of instability corresponds to a loose rock is presented and its stability is determined by numerical analysis. To investigate the effectiveness of present method the influence of shear strength (c, φ) and geometric parameters (α, β) on the safety factor (FS) is also analyzed by using Geo5, FLAC3D and ABAQUS computer codes. Then, Geo5 and Statistical Package for the Social Sciences (SPSS) softwares were used to determine the effect of dimensionless parameter lambda (λ) on the failure surface entry point distance (le) and length of failure arc (L). The results show that shear failure may occur in non-homogeneous slope. Shear failure has exit and entry points situated either on the surface or near the toe of slope. The length of failure arc (L) is affected by the le and λ. Moreover, it can be acknowledged that the relation of both L and le with shear strength parameters (c, φ) is logarithmic, respectively. So, based on the rock strength parameters, L and le are predictable by using the equations derived from non-linear regression.

HDG Methods for Stokes Equation Based on Strong Symmetric Stress Formulations

We propose a hybridizable discontinuous Galerkin (HDG) method for Stokes equation based on strong symmetric stress formulations. Stress-based method stands out compared to gradient or vorticity-based methods by its simple and natural way of enforcing Neumann type boundary conditions. Our method uses the polynomial spaces of orders $${\text {k}}-({\text {k}}+1)-{\text {k}}$$ for the stress–velocity–pressure triplet, and orders $${\text {k}}-({\text {k}}+1)$$ for the tangential and the normal components of the numerical trace space. By sending the normal stabilization to infinity, we obtain another method that provides exactly divergence-free solution and is pressure-robust. We prove that both methods are optimal for all variables and achieve super-convergence for the numerical trace. In addition, we build a quantitative connection between the normal stabilization and the pressure-robustness. Numerical experiments are also presented to validate our theoretical discoveries.

Microstructural Stress Shape Optimization Using the Level Set Method

Abstract This paper applies stress-based shape optimization to microstructures, a scarcely explored topic in the literature. As the actual stresses arising at the macroscopic structure are scale separated, the microstrucural stress is considered herein as the state of a representative volume element (RVE) after applying test unit strain load cases, not related to the macroscale loads. The three stress states in 2D are aggregated via p-norm functions, which are used for stress minimization. A stress-based level set method is applied. The method linearizes the objective and constraint functions and solves an optimization problem at every iteration to obtain the boundary velocities. The Ersatz material approach is used to compute the stiffness of the elements sliced by the boundary. A single hole inclusion microstructure is optimized for minimum stress in order to verify the methodology.

Finite element implementation of coupled temperature-rate dependent fracture using the phase field model

In this paper, a coupled temperature-rate dependent fracture of ductile materials is investigated using a phase field model. The model is proposed based on the strain energy of materials, in contrast to a stress-based method, to follow paths of possible cracks through adding a scalar field as the phase field variable. In this case, two sets of governing equations account in the displacement and phase field are obtained, then solved using the nonlinear finite element method and an implicit integration algorithm. The model is implemented in ABAQUS commercial finite element code through a user element subroutine (UEL). The effects of temperature and loading rate on the initiation and propagation of cracks for ductile solids are examined based on the von Mises criterion. Besides, the threshold parameter as a function of temperature is presented to control the effect of plastic deformation on cracks initiation and propagation for different temperature levels. Moreover, new equations are suggested for the initiation and propagation of cracks as a function of temperature when temperature levels are lower and higher than the ductile-brittle transition temperature. Finally, the influence of loading rates and temperatures on the responses of different specimens is evaluated using the proposed model. The comparison of obtained results with other experimental and numerical data confirms the accuracy of the suggested model. The results also verify that the new model can simulate the influence of lower temperatures on cracks’ paths in which the change of the fracture phase from ductile to brittle occurs.

An approach for the application of energy-based liquefaction procedure using field case history data

This paper presents an overview to the applicability of the “energy-based liquefaction approach” with regards to the new developments in the subject. The method involves comparing the strain energy for the soil liquefaction (capacity) with the strain energy imparted to the soil layer during an earthquake (demand). The performance of the method was evaluated by using a large database of SPT-based liquefaction case history. The energy-based method and the more commonly used stressbased method were compared in their capability to assess liquefaction potential under the same damaging historic earthquakes and geotechnical site conditions. In the procedure, the predictive strain energy equations were used to estimate the capacity energy values. These empirical equations have been developed based on the initial effective soil parameters. As for the energy of any given strong ground motion, it was computed from a velocity-time history of the ground motion and the unit mass of soil through utilization of kinetic energy concepts. The proposed energy-based method has effective way in evaluating the liquefaction potential based on the seismological parameters, contrary to the stress-based approach, where only peak ground acceleration (PGA) is considered.

ARSPivot, A Sensor-Based Decision Support Software for Variable-Rate Irrigation Center Pivot Systems: Part B. Application

HighlightsThe ARSPivot software facilitates variable-rate irrigation management of a center pivot irrigation system.The software embodies a system capable of generating site-specific prescription maps based on weather, plant, and soil water information.ARSPivot’s graphical user interface (GUI) incorporates easy-to-use geographic information system (GIS) tools that help its users to make irrigation management decisions.Abstract. The ARSPivot software was developed for the seamless operation of a complex network consisting of a variable-rate irrigation (VRI) center pivot system and an Irrigation Scheduling Supervisory Control and Data Acquisition (ISSCADA) system that interfaces with weather, plant, and soil water sensing systems. ARSPivot’s graphical user interface (GUI) incorporates a built-in geographic information system (GIS) that maps a center pivot system and facilitates the analysis of data relevant to its operation. The GIS was developed following a minimalistic approach with the objective of making its geospatial data analysis tools accessible to a wide range of users (farmers, irrigation consultants, and researchers). The post-harvest analyses of two experiments carried out in the Texas High Plains during the summers of 2016 and 2017 using a three-span VRI center pivot are presented to illustrate the advantages of using ARSPivot as a decision support tool and how its GIS tools help its users make better informed decisions regarding irrigation management. In these experiments, the north-northwest (NNW) portion of a field planted with corn (Zea mays L.) was irrigated using VRI zone control, and the south-southeast (SSE) portion was irrigated using VRI speed control. Experimental plots in the NNW portion were assigned one of three irrigation levels (80%, 50%, or 30% replenishment of soil water depletion to field capacity in the top 1.5 m), and their irrigation was scheduled using either a plant stress-based algorithm implemented in the ARSPivot software or manual weekly neutron probe (NP) readings. Plots in the SSE portion were assigned a single irrigation level of 80%, and their irrigation was scheduled using either the plant stress method or a two-step hybrid approach in which soil water sensing was combined with the plant stress method to determine irrigation depths. Soil water sensing data for the ISSCADA system were provided by NP readings during the 2016 season and by sets of time-domain reflectometers (TDRs) installed at depths of 15, 30, and 45 cm during the 2017 season. No significant differences were found during either season in terms of mean dry grain yield and crop water productivity (CWP) obtained from plots irrigated at the 80% level in both sides of the field, regardless of the irrigation scheduling method or the type of VRI application method used for irrigation. No significant differences were found during either season between mean dry grain yield and CWP of plots in the NNW portion irrigated using the plant stress-based method and NP readings at the 80% irrigation level. The lack of significant differences documented the potential of the ARSPivot system as a plant and soil water sensing-based decision support software for site-specific irrigation management of corn using a VRI center pivot system. Keywords: Center pivot irrigation, Decision support system, Geographic information system, Precision agriculture, Software.

An equivalent stress method to account for local buckling in beam finite elements subjected to fire

Purpose The purpose of this paper is to present an improved temperature-dependent constitutive model for steel that accounts for local instabilities of slender plates using an effective stress-based method. This model can be easily implemented for use with Bernoulli beam finite elements (FEs) in the fire situation. Design/methodology/approach The constitutive model is derived by calibration on parametric numerical analysis on isolated plates subject to buckling at different elevated temperatures. The model is implemented in the FE software SAFIR and validation is performed against experimental and shell element analysis results. Findings A constitutive model based on an equivalent stress method is proposed as an efficient way to consider local buckling in steel members exposed to fire. The proposed stress–strain–temperature relationship is asymmetric and is modified in compression only, by reducing the proportional limit, the yield stress and the strain at yield stress. The reduction of these parameters depends on the plate’s boundary conditions, slenderness and temperature. The validation of the proposed model shows good agreement over a range of profile dimensions, temperatures and steel grades. Research limitations/implications The model is still giving conservative results for large compressive load eccentricities. An enhanced model is under development to improve the predictive capability under large eccentricities. Practical implications The proposed model, easily implemented into any finite element software, allows using fibre type (Bernoulli) beam FEs for modelling structures made of slender sections. This has major practical implications as beam elements are the workhorse used for simulating the behaviour of structures in fire. This model, thus makes it possible to simulate large structures with slender steel sections at a limited computational cost. Originality/value The paper presents a novel steel constitutive model based on an innovative approach to capture local buckling at the material level using an equivalent stress approach. The theoretical development, validation and perspectives for future improvements are presented.