Variation Of Normal Stress Research Articles

Cyclic deformation behaviour of natural K 0-consolidated soft clay under different stress paths

Characteristic of cyclic loading due to passing wheels is associated with one-way loading without stress reversal, which includes a simultaneous cyclic variation of vertical normal stress and horizontal normal stress lasting for a long period of time and generally takes place in partially-drained conditions. Therefore, it is of great practical relevance to study the deformation behaviour according to the characteristic of traffic loading. In this work, a series of one-way stress-controlled cyclic triaxial tests with a simultaneous variation of the vertical and horizontal stress components during cyclic loading were conducted to investigate the deformation behaviour of natural K0-consolidated soft clay in partially-drained conditions. Test results demonstrate that not only the deviator part of the stress rules accumulation but also the volumetric part significantly contributes. While the deviator part of the stress amplitude is held constant, the increase amplitude of cyclic confining pressure will promote the development of both permanent volumetric strain and axial strain significantly. Furthermore, the effects of cyclic confining pressure on the deformation of natural K0-consolidated soft clay was quantified. Finally, an empirical formula for permanent axial strain considering the effects of cyclic confining pressure was proposed which can be used for feasibility studies or for the preliminary design of foundations on K0-consolidated soft clay subjected to traffic loading.

Design analysis of sandwiched structures experiencing differential thermal expansion and differential free-edge stretching

Compared to the theory of elasticity solutions the strength of material solutions offer closed form solutions that is favoured by practising engineers for performing design analysis. However, the existing strength of material solutions for a sandwich structure experiencing differential thermal strains have principally ignored the free edge conditions; and for the very limited publications that have enforced the free edge conditions, the solutions have been inaccurate. Understandably, design analysis using such solutions is unreliable. This manuscript describe a solution technique that enforces the nil shear stress condition at the free edge using a high power exponential function resulting in a simple yet accurate closed form solutions for the interfacial shear stress. The interfacial peeling stress is made up of two components: the mean and the amplitude of variations of the transverse normal stress in the bonding layer; the latter is the dominant component whose magnitude is linearly proportional to the gradient of the interfacial shear stress. Following validation by finite element analysis, design analysis for debonding, fracturing, and out-of-plane deformation are performed using the concise closed form solutions.

A multilayered plate theory with transverse shear and normal warping functions

A multilayered plate theory taking into account transverse shear and normal stretching is presented. The theory is based on a seven-unknowns kinematic field with five warping functions. Four warping functions are related to the transverse shear, the fifth to the normal stretching. The warping functions are issued from exact three-dimensional solutions. They are related to the variations of transverse shear and normal stresses computed at specific points for a simply supported bending problem. Reddy, Cho–Parmerter and (a modified version of) Beakou–Touratier theories have been retained for comparisons. Extended versions of these theories, able to manage the normal stretching, are also considered. These theories, which use the same kinematic field with different warping functions, are compared to analytical solutions for the bending of simply supported plates. Various plates are considered, with special focus on low length-to-thickness ratios: an isotropic plate, two homogeneous orthotropic plates with ply orientation of 0° and 5°, a [0/c/0] sandwich panel and a [-45/0/45/90]s composite plate. Results show that models are more accurate if their kinematic fields (i) depend on all material properties (not only the transverse shear stiffnesses), (ii) depend on the length-to-thickness ratios and (iii) present a coupling between the x and y directions.

Timing of water plume eruptions on Enceladus explained by interior viscosity structure

Water plume eruptions on Saturn’s icy moon Enceladus are delayed relative to the peak tidal stresses. Simulations suggest the delay can be explained by the moon’s interior structure and the presence of a subsurface ocean. At the south pole of Saturn’s icy moon Enceladus, eruptions of water vapour and ice emanate from warm tectonic ridges1,2,3,4. Observations in the infrared5 and visible6 spectra have shown an orbital modulation of the plume brightness, which suggests that the eruption activity is influenced by tidal forces. However, the observed activity seems to be delayed by several hours with respect to predictions based on simple tidal models6,7. Here we simulate the viscoelastic tidal response of Enceladus with a full three-dimensional numerical model8,9 and show that the delay in eruption activity may be a natural consequence of the viscosity structure in the south-polar region and the size of the putative subsurface ocean. By systematically comparing simulations of variations in normal stress along faults with plume brightness data, we show that the observed activity is reproduced for two classes of interior models with contrasting thermal histories: a low-viscosity convective region above a polar sea extending about 45°–60° from the south pole at a depth below the surface as small as 30 km, or a convecting ice shell of 60–70 km in thickness above a global ocean. Our analysis further shows that the eruption activity is controlled by the average normal stress applied across the cracks, thus providing a constraint on the eruption mechanism.

Determination of normal and shear residual stresses from fracture surface mismatch

Abstract The contour method of residual stress measurement has recently been adapted to measure fractured, rather than cut specimens. The fracture contour method was capable of determining normal residual stresses acting prior to the plane-strain failure of a large aluminium alloy forging, but shear residual stresses could not be measured (Prime et al., 2014). We demonstrate that the application of digital image correlation to topographic measurements of a fracture surface pair allows the determination of shear residual stresses in addition to the normal stress component. Miniature compact tension samples were extracted at an angle from a bent beam to give a known variation in normal and shear residual stress on the fracture plane. The material used was a metal matrix composite, which could be deformed plastically to introduce a known distribution of stresses and also present limited plasticity upon fracture, allowing plane-strain condition in a small specimen. The samples were fractured at cryogenic temperatures to further restrict plasticity. Although the fracture surface was non-planar and evidence suggested the occurrence of plasticity near the edges, experimental results correlated fairly well with the calculated normal and shear residual stress profiles.

Spine growth and seismogenic faulting at Mt. Unzen, Japan

AbstractThe concluding episode of activity during the recent eruption of Mt. Unzen (October 1994 to February 1995) was characterized by incremental spine extrusion, accompanied by seismicity. Analysis of the seismic record reveals the occurrence of two dominant long‐period event families associated with a repeating, nondestructive source mechanism, which we attribute to magma failure and fault‐controlled ascent. We obtain constraints on the slip rate and distance of faulting events within these families. That analysis is complemented by an experimental thermomechanical investigation of fault friction in Mt. Unzen dacitic dome rock using a rotary‐shear apparatus at variable slip rates and normal stresses. A power density threshold is found at 0.3 MW m−2, above which frictional melt forms and controls the shear resistance to slip, inducing a deviation from Byerlee's frictional law. Homogenized experimentally generated pseudotachylytes have a similar final chemistry, thickness, and crystal content, facilitating the construction of a rheological model for particle suspensions. This is compared to the viscosity constrained from the experimental data, to assess the viscous control on fault dynamics. The onset of frictional melt formation during spine growth is constrained to depths below 300 m for an average slip event. This combination of experimental data, viscosity modeling, and seismic analysis offers a new description of material response during conduit plug flow and spine growth, showing that volcanic pseudotachylyte may commonly form and modify fault friction during faulting of dome rock. This model furthers our understanding of faulting and seismicity during lava dome formation and is applicable to other eruption modes.

Analytical higher-order model for flexible and stretchable sensors

The stretchable sensor wrapped around a foldable airfoil or embedded inside of it has great potential for use in the monitoring of the structural status of the foldable airfoil. The design methodology is important to the development of the stretchable sensor for status monitoring on the foldable airfoil. According to the requirement of mechanical flexibility of the sensor, the combined use of a layered flexible structural formation and a strain isolation layer is implemented. An analytical higher-order model is proposed to predict the stresses of the strain-isolation layer based on the shear-lag model for the safe design of the flexible and stretchable sensors. The normal stress and shear stress equations in the constructed structure of the sensors are obtained by the proposed model. The stress distribution in the structure is investigated when bending load is applied to the structures. The numerical results show that the proposed model can predict the variation of normal stress and shear stress along the thickness of the strain-isolation (polydimethylsiloxane) layer accurately. The results by the proposed model are in good agreement with the finite element method, in which the normal stress is variable while the shear stress is invariable along the thickness direction of strain-isolation layer. The high-order model is proposed to predict the stresses of the layered structure of the flexible and stretchable sensor for monitoring the status of the foldable airfoil.

FEM Hydroelastic Models with Application to the Nonlinear Response of Large Floating Bodies in Shallow Wave Conditions

Abstract A higher order finite element scheme is presented for the study of the transient hydroelastic response of a floating, thin, nonlinear strip in shallow wave conditions. First, nonlinear effects are introduced only in the elasticity model, where large deflections and non-negligible normal stress variation in the lateral direction are assumed. The nonlinear beam is initially coupled with the linearized and subsequently with the full nonlinear Shallow Water equations, introducing nonlinearity in both the hydrodynamics and the elasticity model. The effects of the incorporated nonlinear effects are assessed through a numerical example featuring an elevation pulse of increasing steepness.

Effect of varying normal stress on stability and dynamic motion of a spring-slider system with rate- and state-dependent friction

Incorporating rate and state friction laws, stability of linearly stable (i.e., with stiffness greater than the critical value) spring-slider systems subjected to triggering perturbations was analyzed under variable normal stress condition, and comparison was made between our results and that of fixed normal stress cases revealed in previous studies. For systems associated with the slip law, the critical magnitude of rate steps for triggering unstable slips are found to have a similar pattern to the fixed normal stress case, and the critical velocity steps scale with a/(b − a) when k = kcr for both cases. The rate-step boundaries for the variable normal stress cases are revealed to be lower than the fixed normal stress case by 7 %–16 % for a relatively large α = 0.56 with (b − a)/a ranging from 0.25 to 1, indicating easier triggering under the variable normal stress condition with rate steps. The difference between fixed and variable normal stress cases decreases when the α value is smaller. In the same slip-law-type systems, critical displacements to trigger instability are revealed to be little affected by the variable normal stress condition. When k ≥ kcr(V*), a spring-slider system with the slowness law is much more stable than with the slip law, suggesting that the slowness law fits experimental data better when a single state variable is adopted. In stick-slip motions, the variable normal stress case has larger stress drops than the constant normal stress case. The variable normal stress has little effect on the range of slip velocity in systems associated with the slowness law, whereas systems associated with the slip law have a slowest slip velocity immensely smaller than the fixed normal stress case, by ~10 orders of magnitude.

Finite element simulations of notch tip fields in magnesium single crystals

Recent experiments using three point bend specimens of Mg single crystals have revealed that tensile twins of {10 (1) over bar2}-type form profusely near a notch tip and enhance the fracture toughness through large plastic dissipation. In this work, 3D finite element simulations of these experiments are carried out using a crystal plasticity framework which includes slip and twinning to gain insights on the mechanics of fracture. The predicted load-displacement curves, slip and tensile twinning activities from finite element analysis corroborate well with the experimental observations. The numerical results are used to explore the 3D nature of the crack tip stress, plastic slip and twin volume fraction distributions near the notch root. The occurrence of tensile twinning is rationalized from the variation of normal stress ahead of the notch tip. Further, deflection of the crack path at twin-twin intersections observed in the experiments is examined from an energy standpoint by modeling discrete twins close to the notch root.

Source scaling relations and along‐strike segmentation of slow slip events in a 3‐D subduction fault model

AbstractScaling between slip event duration and equivalent moment is diagnostic of the underlying physics of rupture process. For episodic slow slip events (SSEs) in subduction zones, their moment‐duration relation is not clearly defined and shows considerable variation among individual margins where multiple episodes of SSEs are geodetically detected. Here I set up a 3‐D planar thrust fault model within the framework of rate‐state friction to study the spatiotemporal evolution of slip and stress during SSEs. SSE source properties, including along‐strike length, duration, equivalent moment, and stress drop, are quantified, and their scaling relations are compared to observations. Modeled SSEs have nearly constant stress drops of 0.001 to 0.01 MPa, due to near‐lithostatic pore pressure at the SSE depths. The modeled moment‐duration scaling is between 1 (linear) and 2 (squared). When multiple SSEs appear simultaneously along the strike, the stress interaction between approaching slip fronts results in higher average propagation speeds for longer lengths, which leads to a scaling close to 2. When SSEs are well offset in space and time, stress interaction is negligible and the scaling is close to 1. Two types of SSE along‐strike segmentation gaps are identified from model results. The “primary” gaps are persistent segmentation boundaries due to along‐strike variation of effective normal stress, while the “secondary” gaps evolve through SSE cycles and reflect the stress condition within a primary segment. This implies that some geodetically inferred SSE segmentation boundaries may result from slower slip velocities below the resolution limits of geodetic inversion models.

Study on the hydromechanical behavior of single fracture under normal stresses

The coupling between hydraulic and mechanical behavior of the fractured rock mass is of great significance for various civil and environmental engineering projects. In order to study the hydro-mechanical behavior of single fracture, seepage tests under different confining pressures and fracture water pressures were conducted on single shear fractures produced by triaxial loading of diabase rock samples from Danjiangkou Water Reservoir, China. Test results show that fluid pressure acting on fracture surfaces has strong influences on the hydraulic behavior of the fracture. Based on the classic Biot poroelasticity theory and by taking the fracture as assembling of a set of voids in rock mass, a generalized Biot coefficient is introduced to describe the interaction effect between pore fluid pressure and fracture deformation. Then, a nonlinear constitutive equation for single fracture under both normal stress and fluid pressure is developed. Later, the mechanical deformation of the fracture is related to the fracture hydraulic conductivity through “cubic law”, so that a coupled mechanical-hydraulic model is proposed. All the four parameters involved in this model have their physical significances and can be determined through mechanical compression tests and seepage tests. A first validity of the model is made by predicting the variation of fracture flowrates versus normal stress under different fluid pressures.

Numerical Study on Normal Stress Distributions in a Single-Lap Adhesive Joint

Adhesively bonding is becoming a widespread candidate technique for joining light-weight structural components. This paper investigates normal stress distribution in a single-lap adhesive joint using finite element method. Five layers of solid elements were used across the adhesive for obtaining an accurate indication of the variation of normal stress. All the numerical results obtained from the finite element analysis show that the spatial distribution of normal stress are similar for different interfaces. It can also be seen from the results that the left hand region is subjected to very high stress.

입자법을 이용한 토사의 대변형 해석법 개발

본 연구에서는 토사 유동과 같은 대변형 해석을 위해 기존 유한요소법이나 유한차분법과 달리 격자를 사용하지 않는 입자법을 사용하였으며, 입자법은 구배, 발산, 라플라시안과 같은 미분연산자에 대응하는 입자간 상호작용모델을 이용하여 연속체의 지배방정식을 이산화하였다. 외부 하중이나 함수비 증가에 따라 고체에서 유체 상태로 변하는 흙의 3차원 대변형 거동을 해석하기 위해 기존 입자법에 흙의 파괴상태를 고려할 수 있는 Mohr-Coulomb 파괴기준을 도입하였으며, 흙의 파괴 이전의 항복이나 경화현상으로 인한 대변형은 흙을 점성 유체로 가정하여 해석하였다. 개발된 입자법은 먼저 구속압이 작용하지 않고 강도가 0인 모래기둥 붕괴실험 결과를 이용하여 검증한 다음, 점착력을 가지고 자립이 가능한 점토기둥 붕괴실험을 실시하여 흙의 항복이나 파괴로 인한 대변형을 시뮬레이션하였다. 개발된 입자법은 모래와 점토의 3차원 대변형 거동을 유사하게 잘 예측하였으며, 파괴 이전에 발생하는 흙의 항복으로 인한 소성변형에 따른 흙기둥 내의 수직 및 전단응력 변화도 계산할 수 있었다. In this study, a particle method without using grid was applied for analysing large deformation problems in soil flows instead of using ordinary finite element or finite difference methods. In the particle method, a continuum equation was discretized by various particle interaction models corresponding to differential operators such as gradient, divergence, and Laplacian. Soil behavior changes from solid to liquid state with increasing water content or external load. The Mohr-Coulomb failure criterion was incorporated into the particle method to analyze such three-dimensional soil behavior. The yielding and hardening behavior of soil before failure was analyzed by treating soil as a viscous liquid. First of all, a sand column test without confining pressure and strength was carried out and then a self-standing clay column test with cohesion was carried out. Large deformation from such column tests due to soil yielding or failure was used for verifying the developed particle method. The developed particle method was able to simulate the three-dimensional plastic deformation of soils due to yielding before failure and calculate the variation of normal and shear stresses both in sand and clay columns.

2D numerical simulation of submerged hydraulic jumps

Hydraulic jumps are usually used to dissipate energy in hydraulic engineering. In this paper, the turbulent submerged hydraulic jumps are simulated by solving the unsteady Reynolds averaged Navier–Stokes equations along with the continuity equation and the standard k–ɛ equations for turbulence modeling. The Lagrangian moving grid method is employed for the simulation of the free surface. In the developed model, kinematic free-surface boundary condition is solved simultaneously with the momentum and continuity equations, so that the water elevation can be obtained along with velocity and pressure fields as part of the solution. Computational results are presented for Froude numbers ranging from 3.2 to 8.2 and submergence factors ranging from 0.24 to 0.85. Comparisons with experimental measurements show that numerical model can simulate the velocity field, variation of free surface, maximum velocity, Reynolds shear and normal stresses at various stations with reasonable accuracy.

Application of the method of nonplanar sections to determine stresses in the zones of concentration caused by weld reinforcement in butt-welded joints

A procedure for determining stresses in butt-welded joints, which is based on the hypothesis of nonplanar sections, has been justified. The analytical expressions describing the variation of normal stresses in the concentration zone both over the contour and the depth of the joint have been obtained. At the point, where the concentration reaches its maximum value, the expression for calculating the stress concentration factor has been derived. The results from the calculation of the stress concentration factor are compared with those in references. The expressions for determining both the stress gradient at any point in the section, which is beyond the stress concentration zone, and the relative stress gradient at the point where the stress attains its maximum value have been obtained.

RSQSim Earthquake Simulator

As discussed in Tullis et al. (2012b), a promising avenue for improving seismic hazard estimation and reducing the large uncertainties in current assessments is to incorporate more accurate and region‐specific characterizations of the interactions and physical processes that control earthquake occurrence in fault systems. Earthquake simulators are computer models that can contribute to this by carrying out large‐scale simulations of earthquake occurrence to characterize system‐level response of fault systems including processes that control time, place, and extent of earthquake slip. Such simulators were pioneered by work such as Rundle (1988), Robinson and Benites (1995), and Ward (1996). Four such simulators are discussed in the November/December 2012 Seismological Research Letters issue, and their general features are described in Tullis et al. (2012a). This paper describes features specific to one of those four, RSQSim. It also presents results that are relevant to particularly unique features of RSQSim: comparisons with fully dynamic single‐event simulations and the spatial‐temporal clustering of seismicity due to RSQSim’s use of rate‐ and state‐dependent friction (RSF). RSQSim is based on a scheme initially developed by Dieterich (1995) with several enhancements to extend its use in a number of directions including allowing fully general fault system geometries and the attendant normal stress variations, better validation of the quasi‐dynamic part of the seismic cycle against fully dynamic models, and the inclusion of creeping parts of the fault system. Ziv (2003) and Ziv and Rubin (2003) used some elements of the original method to study clustering processes and frequency statistics. RSQSim itself has been used by Dieterich and Richards‐Dinger (2010) to study the effects of both small‐ and large‐scale fault system geometry on recurrence statistics in a idealized but complex fault system. We do not discuss it further here, but RSQSim has also been used successfully to model slow …

Seasonal movement and groundwater flow mechanism in an unsaturated saprolitic hillslope

Numerous field monitoring programs have been conducted to investigate the performance of an unsaturated soil slope subjected to rainfalls in wet seasons. Most case histories focus on the response of matric suction, which is one of the two stress-state variables governing unsaturated soil behaviour. However, effects due to another variable, net normal stress, are often ignored. Also, slope performance under alternative wet and dry seasons is rarely reported and analysed. In this study, a saprolitic hillslope situated in Hong Kong was instrumented heavily to investigate its seasonal movement due to changes of the two variables and also groundwater flow mechanism. Two-year seasonal variations of matric suction and net normal stress were monitored by tensiometers together with heat dissipation matric water potential sensors and earth pressure cells, respectively. During heavy rainstorms in wet season, there was a substantial recharge of the main groundwater table, causing a significant increase of positive pore-water pressure in deeper depths. Rupture surface likely developed at depths between 5.5 and 6 m, hence resulting in a “deep-seated” mode of downslope movement. The downslope movement resulted in a peak increase of horizontal stress. In dry seasons, matric suction of up to 190 kPa was recorded, and the associated soil shrinkage led to substantial upslope rebounds. The stress built up in wet seasons hence reduced. After monitoring period of 2 years, downslope ratcheting is identified. Up to 40 % of the downslope displacements were recovered by the upslope rebounds.

FLAC Based Numerical Studies on Dynamic Interference of Two Nearby Embedded Machine Foundations

This paper emphasizes on the dynamic interaction of two closely spaced embedded square or rectangular foundations under the action of machine vibration. One of the foundations is excited with a known vibration source placed on the top of it, called the active foundation. The objective is to study the effect of dynamic motion of the active foundation on the nearby passive foundation through a layered soil medium. The analysis is performed numerically by using the explicit finite difference code FLAC 3D . The soil profile is assumed to obey the Mohr–Coulomb yield criteria with non-linear failure envelope. The analysis is performed under sinusoidal dynamic loading with varying amplitude. Under the dynamic excitation, the settlement behavior of the interacting foundations is studied by varying the spacing between the foundations. In addition, the variation of vertical normal and shear stress developed beneath the interacting foundations is also explored. The present theoretical investigation indicates that the settlement and vertical normal stress below the active foundation is generally found to be higher than that obtained for the passive foundation, whereas the shear stress response below the foundations follows the reverse trend.

Normal Stress Distributions in a Single-Lap Adhesively Bonded Joint under Tension

This paper investigates normal stress distribution of a single-lap adhesively bonded joint under tension using the three-dimensional finite element methods. Five layers of solid elements were used across the adhesive layer thickness in order to obtain an accurate indication of the variation of normal stress. All the numerical results obtained from the finite element analysis show that the spatial distribution of normal stress are similar for different interfaces though the stress values are obviously different. It can also be seen from the results that the left hand region, which is very close to the left free end of the adhesive layer, is subjected to very high stress and the magnitude of the normal stress oscillates in value close to the left end of the adhesive layer.