Vertical Stress Component Research Articles

An analytical investigation of soil arching induced by tunneling in sandy ground

The soil mass above the tunnel generally yields due to the tunnel volume loss. Depending on the amount of the volume loss, soil unit weight, overburden height and internal friction angle, a stress arching zone and a loosened zone can be formed above the tunnel. In this study, a two-dimensional stress field resulting from the tunnel volume loss inside the soil mass above the tunnel is investigated analytically. By presenting an analytical solution in rectangular coordinates, new equations were developed to evaluate and estimate the magnitude of vertical, horizontal and shear stress components inside the soil mass. The vertical stress changes resulting from the tunnel volume loss were analyzed and the height of the arching zone and the loosened zone above the tunnel were determined. In addition, a parametric study was conducted to evaluate the effect of soil unit weight, soil internal friction angle, surcharge on the ground surface and overburden depth on the stress distribution in the soil above the tunnel. The results showed that depending on the depth of the tunnel and the strength of the surrounding soil, the arching and loosened zones may or may not be created. In order to validate the proposed solution, the vertical stress distribution along the tunnel crest has been compared with some experimental and numerical data. It can be stated that the proposed solution provides relatively good approximations for the vertical stress component. The results of this research show that a safe and economical support system for tunnels in sandy ground can be designed using the proposed solution.

Геомеханическое обоснование формирования зон хрупкого разрушения пород в окрестности сопряжений горных выработок рудников АО «Апатит»

Introduction. Prediction of excavations stability is an important step towards ensuring geo-mechanical safety during their construction. A reliable prediction of the stability of excavations includes such factors as the initial stress state, physical and mechanical characteristics of rocks, rock mass fracturing, and a number of others. These factors should be considered when performing calculations. The geo-mechanical conditions of the Apatite deposits are different, rock pressure can manifest itself in the form of brittle fracture of rocks, limited displacement of the rock contour, the formation of local rock failures or arching. In this paper, we consider only areas of the rock mass, where the loss of stability of the excavation contour is associated with the formation of brittle fracture zones. An analysis of methods for predicting brittle fracture zones suggests that they are devoted to their formation in the vicinity of single excavation and do not consider the formation of brittle fracture zones in the areas of excavation junctions. Despite the fact that a significant number of research papers are devoted to the formation of plastic deformation zones and the assessment of the excavation contour stability, they mainly consider two forms of geo-mechanical processes - rock failure along fractures and rock contour deformations. At the same time, little attention is paid to the formation of brittle fracture zones in the areas of excavation junctions in rocks predisposed to the development of such geo-mechanical processes. Considering the conditions of the Apatite deposits, it can be noted that the values of deformational and strength characteristics of rocks are very high. The rock mass is different in fracturing characteristics, however, the volume of rocks with excavations, which can be classified as weakly fractured, is very significant. The initial stress state of rock mass is characterized by the tectonic nature, where the magnitudes of the largest horizontal stresses are several times greater than the vertical stress component. All this makes it possible to classify the conditions of Apatite deposits as very difficult and rock burst hazardous. Methods and materials. To assess the correctness of the numerical modeling using model of brittle fracture of rocks, the following typical problems are considered: forecasting the development of brittle fracture zones in the vicinity of excavations of research laboratory in Canada; forecast of zones of brittle fracture of rocks for mining-geological and geo-mechanical conditions of the Apatite enterprises. Numerical modeling and the stress-strain state prediction in the vicinity of excavations was carried out in a generalized plane-strain formulation (three-dimensional formulation with the assignment of appropriate boundary conditions). An analysis of numerical simulation results suggests that the increase in the size of the brittle fracture zone is that greater, the larger the junction span. This effect was obtained for all four variants of excavation junction. The following results of the stress-strain state formation in rock mass in the vicinity of excavation junctions were obtained: the size of the brittle fracture zone as a whole tends to increase in the areas of excavation junctions, while the type of junction plays a significant role in its size; the higher the value of the σmax index, the more clearly the influence of the junction type on the size of the brittle fracture zone is manifested, while at the ratio σmax/σc < 0.8, the difference in the sizes of the zones in the junction and the extended section of the excavation is not significant. It was noted that the excavation junction has an impact not only on the size of the brittle fracture zone, but also on the nature of this zone formation. There is a “flow” of the brittle fracture zone from the junction area directly to the single excavation, the direction of which coincides with the direction of the maximum principal stresses. Thus, it is possible to form rock failure in the excavation located in a moderately stressed rock mass; The proposed model for predicting brittle fracture zones based on setting the functions of hardening/softening of the medium, makes it possible to effectively predict brittle fracture zones in the vicinity of excavation junctions. In general, the research results confirm the patterns of brittle fracture zones development in the vicinity of excavation junctions obtained by the authors, however, an improved model for describing the development of geo-mechanical processes in rocks prone to brittle fracture made it possible to significantly increase the reliability of predicting the shape of the brittle fracture zone near the excavation.

Hydrodynamic Characteristics of Diagonal Brush Fish Pass: Prototype Measurements

The present study investigates the hydrodynamic characteristics of the diagonal brush upstream fishway at the Incirli run-of-river hydropower plant on Iyidere River in Turkey. Three-dimensional velocity measurements were conducted in the fish pass using a Micro acoustic Doppler velocimeter under real-time operation conditions. The diagonal arrangement of brush blocks creates favorable hydrodynamic conditions (i.e., lateral momentum exchange) that allow fish to minimize swimming energy. We found that the spatially averaged lateral component of Reynolds shear stress is 2.2 times higher than spatially averaged vertical component of Reynolds shear stress, which could be due to the lateral velocity gradient in the vicinity of brush blocks. It is shown that the low-velocity zones behind the brush blocks constitute important resting sites for fish. The monitoring data showed that inlet water levels have considerable effects on the turbulence quantities. The brushes become submerged with the increased reservoir water level from 102 m to 102.05 m above sea level. The maximum turbulent kinetic energy was increased by a factor of three compared to unsubmerged conditions. We found a strong relationship between the average energy dissipation rate per unit mass and the Reynolds number. On the other hand, the prototype data reveal the inverse relationship between the Darcy-Weissbach friction factor and the relative submergence of bristles. The present results allow the efficient design of diagonal fish passes.

Use of machine learning algorithms to assess the state of rockburst hazard in underground coal mine openings

The risk of rockbursts is one of the main threats in hard coal mines. Compared to other underground mines, the number of factors contributing to the rockburst at underground coal mines is much greater. Factors such as the coal seam tendency to rockbursts, the thickness of the coal seam, and the stress level in the seam have to be considered, but also the entire coal seam–surrounding rock system has to be evaluated when trying to predict the rockbursts. However, in hard coal mines, there are stroke or stress-stroke rockbursts in which the fracture of a thick layer of sandstone plays an essential role in predicting rockbursts. The occurrence of rockbursts in coal mines is complex, and their prediction is even more difficult than in other mines. In recent years, the interest in machine learning algorithms for solving complex nonlinear problems has increased, which also applies to geosciences. This study attempts to use machine learning algorithms, i.e. neural network, decision tree, random forest, gradient boosting, and extreme gradient boosting (XGB), to assess the rockburst hazard of an active hard coal mine in the Upper Silesian Coal Basin. The rock mass bursting tendency index W TG that describes the tendency of the seam–surrounding rock system to rockbursts and the anomaly of the vertical stress component were applied for this purpose. Especially, the decision tree and neural network models were proved to be effective in correctly distinguishing rockbursts from tremors, after which the excavation was not damaged. On average, these models correctly classified about 80% of the rockbursts in the testing datasets.

FEA of mechanical behaviour of insulated rail joints due to vertical cyclic wheel loadings

Insulated rail joints (IRJs), safety critical components of railway track, are used to locate trains and broken rails using electrical signalling systems. The bending rigidity of the rail at an IRJ is only 2/3rds that of continuous rail. As a result, stress singularity problems occur at IRJs which therefore degrade faster compared to the continuous rail. Both railhead top surface and sub-surface damage occurs and accelerates the initiation of cracks. Head hardened rails are used to overcome these problems.A thorough study addresses the damage pattern in the railhead sub-surface using a 3D finite element analysis (FEA) employing vertical wheel loadings considering three endpost materials: fibre glass (fb), nylon 66 (ny) and polytetrafluoroethylene (ptfe). A new damage parameter, the vertical residual stress component, is proposed to assess new patterns of railhead damage considering plastic deformation. To rank the influential stress related damage parameters, two other parameters are also considered, namely residual von-Mises and longitudinal stress components. Of these, the residual von-Mises stress component is more prominent with regard to the top surface and sub-surface damage, whereas the longitudinal stress component is responsible for top surface material damage. From these damage patterns, a progressive change in the hardness distribution of railhead material can evolve.

Asymmetry of faults and stress patterns within the Dead Sea basin as displayed by seismological analysis

The Dead Sea pull-apart basin (DSB), which is located within the Dead Sea Transform fault system, displays tectonic asymmetry between its eastern and western longitudinal zones. We investigate the seismological and mechanical signature of this asymmetry by the analyzing the hypocenter distribution and focal-mechanisms of 114 Mw = 1.5–5.2 earthquakes recorded from 1985 till 2012. The analysis indicates that the seismicity along the western longitudinal zone is deeper than the eastern one. Focal mechanism analysis indicates that about 50% of solutions are strike-slip, compatible with the plate motions along the Dead Sea transform. Comparison between the two longitudinal zones of the basin shows that the focal mechanisms in the eastern DSB are dominated by strike-slip faulting shallower than 12 km depth, whereas those in the western DSB are dominated by oblique faulting below 12 km depth. The b value of the Gutenberg-Richter magnitude distributions also show difference between the two zones with ~0.9 in the west and ~0.7 in the east zone.We develop stress-inversion analysis to identify the fault planes of the focal mechanisms by using friction-dependent selection process. The horizontal maximum compression (σHmax) trends NNW-SSE, with increasing value of the vertical stress component along the western part of the basin, corresponds to the oblique faulting in this zone. The optimal friction coefficient determined by the stress-inversion for the fault planes is μ ~ 0.5. Our analysis emphasizes the significant contribution of frictional dependent stress-inversion as an effective tool in seismotectonic analysis.

Stress State of a Roadbed Reinforced with Soil-Concrete Layer under the Impact of Heavy-Tonnage Trains

The present paper is aimed at the research into stress state of a roadbed reinforced with a soil-concrete layer and being exposed to the impact of heavy-tonnage trains with axle load of 245-295 kN/axle. To assess the effect of soil-concrete layer on the stress state of the roadbed, multivariable calculation tests were performed via the finite element method. Graphs of equivalent tensile stresses in the models of railroad were obtained, as well as graphs of normal horizontal and vertical stress components that arise in the subgrade of the railroad. The calculation results obtained show that as far as the axle load of a train increases, stress state of a model changes, areas of critical stress values for soils in a railroad’s subgrade grow. In a railroad model that is reinforced with a soil-concrete layer, areas of critical stresses are less than in a non-reinforced model. Allowable stress exceeds in a subgrade when a train with an axle load of 294 kN/axle impacts a railway model of a standard structure. When a roadbed is reinforced with a soil-concrete layer, the stress arising is less than the maximum allowed value. The results obtained allow recommending to use a soil-concrete layer for the reinforcement of roadbeds of railway tracks designed for heavy-tonnage train traffic.

Assessing mechanical response of CO2 storage into a depleted carbonate reef using a site-scale geomechanical model calibrated with field tests and InSAR monitoring data

Geomechanical risks of injection have raised concerns regarding secure CO2 storage. In this work, a combined monitoring and modeling approach is used to assess the stress changes and surface uplift associated with CO2 injection into a depleted carbonate reef of the Michigan basin. A site-scale geomechanical model is built by assigning mechanical properties of formations using well-log and experimental data. Gravity load is applied to the model to estimate the vertical component of stress as well as different lateral boundary displacement scenarios to estimate horizontal stresses. We used a poroelastic pressure-dependent model (instead of a linear elastic mechanical earth model) to calibrate initial stresses using hydraulic fracture test data measured at depleted reservoir status. Multi-phase fluid flow-geomechanical simulations are performed to estimate the poroelastic response during (1) primary depletion (2) field-scale CO2 injection phase (3) a hypothetical forecast scenario in which well bottom hole pressure (BHP) reach 45000 KPa. The predicted surface uplift is less than 1 mm at the end of the field-scale CO2 injection phase which is in good agreement with Interferometric Synthetic Aperture Radar (InSAR) uplift measurement. Although the InSAR data shows an insignificant uplift, hydromechanical modeling of injection shows that CO2 injection still causes reservoir deformation emphasizing the role of carbonate overburden and reservoir formation mechanical properties and limited size of reef on diminishing the surface deformation. Modeling indicates poroelastic response of caprock matters to estimate uplift. The lower permeability of the top two layers provides additional barrier to large uplift. Also, history of subsidence due to production should be accounted to predict uplift due to a follow up injection correctly. This study shows the significance of combining a calibrated geomechanical model with field measured stresses and monitoring data to be used as a tool to ensure the safety of CO2 storage.

On the large- and small-scale motions in a separated, turbulent-boundary-layer flow

ABSTRACTAdverse-pressure-gradient turbulent boundary layer flow was inspected at Reynolds number based on momentum thickness, , using particle image velocimetry in a refractive-index-matching flume. Proper orthogonal decomposition was used to quantify the effect of large-scale motions on the Reynolds stresses at the onset of separation and within the separated flow. Results show that approximately of the Reynolds shear stress, , is due to large-scale motions containing of the turbulence kinetic energy at the tested Reynolds number. The decomposed velocity field revealed that only the first of the modes is sufficient to recover of the turbulence kinetic energy. In this partition, the large-scale motion contribution to the streamwise component of the Reynolds normal stress, , is about and continues to grow with flow separation. In addition, the large- and small-scale motions equally contributed to the vertical component of the Reynolds normal stress, , and the contribution of the large-scale motions increased as the flow separated. Overall, results emphasise the significant impact of the large-scale motions on the Reynolds stresses in the separated flow, which may impact flow control strategies.

Three‐dimensional discrete element method parallel computation of Cauchy stress distribution over granular materials

SummaryThe paper presents Cauchy stress tensor computation over parallel grids of message passing interface (MPI) parallel three‐dimensional (3D) discrete element method (DEM) simulations of granular materials, considering spherical and nonspherical particles. The stress tensor computation is studied for quasi‐static and dynamic conditions, and its resulting symmetry or asymmetry is discussed within the context of classical continuum mechanics (CCM), granular materials mechanics (GMM), and micropolar continuum mechanics (MCM). The average Cauchy stress tensor computation follows Bagi's and Nicot's formulations and is verified within MPI parallel 3D DEM simulations involving dynamically adaptive compute grids. These grids allow calculation of temporal and spatial distributions of stress across granular materials under static and dynamic conditions. The vertical stress component in gravitationally deposited particle assemblies exhibits nonuniform spatial distributions under static equilibrium, and its zone of maximum value changes during the process of gravitational pluviation and collapse. These phenomena reveal a microstructural effect on stress distribution within granular materials that is attributed to their discrete particulate nature (particle size, shape, gradation, boundary conditions, etc).

Observation of the keyhole behavior, spatter, and keyhole-induced bubble formation in laser welding of a steel/glass sandwich

Laser welding of a steel/glass sandwich is carried out to clearly observe the keyhole behavior, spatter, and keyhole-induced bubble formation. The formation mechanisms of the spatter and keyhole-induced bubble are analyzed, and the relationship between the spatter and keyhole-induced bubble formation is also discussed. There are five necessary steps for the spatter formation around the keyhole: the formation of the bulges at the keyhole wall, the decrease of the keyhole entrance size caused by the upward flow of the bulges, the formation of the melt column around the keyhole, the increasing of the melt column size, and the spatter formation around the keyhole. The decrease of the keyhole entrance size contributes to the increase of the vapor shear stress, and thus accelerates the spatter formation. The large deformation of the top rear keyhole wall decreases the vertical component of the vapor shear stress, so few spatters are formed at the rear keyhole wall. Two types of the keyhole-induced bubble are formed by the whole keyhole collapse between the front keyhole wall and rear keyhole wall, and the rear keyhole wall collapse. The influence of the keyhole-induced bubble formation on the spatter formation is not obvious.

Relation between crustal stress and thickness of earth's crust

Available models for estimation of crustal stress consider the vertical stress component as weight of above laying rocks, while horizontal stress components are estimated as function of vertical component. Herein, it is assumed that horizontal stress is effect of strain formed at seismogenic depth and transferred to shallower depth of rock mass. Strain rate is different depending on thickness of the crust and is different in different locations. Using available data regarding the measured maximum horizontal stress and depth of Moho discontinuity trend between these is obtained. Trend shows that maximum horizontal stress is decreasing with the thickness of the Earth’s crust and vice versa. Finally, expression that defines maximum horizontal stress from Moho depth and deformation modulus of rock mass is provided.

Determination of stress components in 4H-SiC power devices via Raman spectroscopy

The stress dependencies of the phonon modes in a 4H silicon carbide (SiC) crystal were investigated. The deformation potentials of the A1(TO), E2, and E1(TO) modes were determined on the basis of uniaxial stress tests. The A1(TO) mode was sensitive to stress along the c axis, whereas the E1(TO) and E2 modes exhibited larger dependencies on the stress perpendicular to the c axis than the A1(TO) mode as expected from their atomic displacements. The coefficient of the frequency shift in the E2 mode for an isotropic biaxial stress in the c plane was determined to be −323 MPa/cm−1. We applied cross-sectional Raman measurements to SiC metal-oxide-semiconductor field-effect transistors. The horizontal and vertical stress components, σ11 and σ33, were derived from the frequency shifts of the E2 and A1(TO) modes using the deformation-potential constants. A compressive horizontal stress was observed near the interface between the SiC chip and the metals. The observed compressive stress increased as the temperature decreased. The main cause for the compressive horizontal stress at low temperature is considered to be the difference in the coefficients of thermal expansion of the SiC chip and the metals. The results suggest that the temperature of the fabrication process is one of the key factors for achieving a reduction in the thermal stress in the SiC power devices.

Cenozoic Shift From Compression to Strike‐Slip Stress Regime in the High Andes at 30°S, During the Shallowing of the Slab: Implications for the El Indio/Tambo Mineral District

AbstractIn the High Andes of central Chile, above the flat‐slab segment, analysis of more than 1,000 fault slip data from Miocene outcrops provides evidence for a change of the regional tectonic regime from compressional to strike slip. This shift in tectonic regime occurred during the waning stages of arc volcanism between 14 and 11 Ma, as a result of the shallowing of the Nazca plate, in conjunction with the migration of deformation to the Precordillera. During the early to middle Miocene, a compressive regime with horizontal σ1 axis (N86°E) was responsible for reverse slip along NNE to N‐striking faults. During the late Miocene, a shift to strike‐slip tectonics took place due to an increase in the absolute magnitude of the vertical stress component as the crust thickened and the gravitational potential energy increase. We argue that instead of the previously accepted highly compressional setting in the arc region during the slab flattening, the change to a strike‐slip regime was the main control on mineralization. Mineralization was controlled by the promotion of fluid expulsion from the magma chambers along active, subvertical strike‐slip fault systems with a high slip tendency, and focusing of fluids in localized areas undergoing extension. Under this strike‐slip regime, the El Indio, Tambo, and La Despensa fault systems formed as dextral strike‐slip systems. The tips and jogsites along these faults experienced local extensional stress fields, forming the El Indio and Tambo mineral districts.

In situ stress conditions at IODP Site C0002 reflecting the tectonic evolution of the sedimentary system near the seaward edge of the Kumano basin, offshore from SW Japan

AbstractThis paper presents a complete set of in situ stress calculations for depths of 200–1400 meters below seafloor at Integrated Ocean Drilling Program (IODP) Site C0002, near the seaward margin of the Kumano fore‐arc basin, offshore from southwest Japan. The vertical stress component was obtained by integrating bulk density calculations from moisture and density logging data, and the two horizontal components were stochastically optimized by minimizing misfits between a probabilistic model and measured breakout widths for every 30 m vertical segment of the wellbore. Our stochastic optimization process reveals that the in situ stress regime is decoupled across an unconformity between an accretionary complex and the overlying Kumano fore‐arc basin. The stress condition above the unconformity is close to the critical condition for normal faulting, while below the unconformity the geologic system is stable in a normal to strike‐slip fault stress regime. The critical state of stress demonstrates that the tectonic evolution of the sedimentary system has been achieved mainly by the regionally continuous action of a major out‐of‐sequence thrust fault during sedimentation in the fore‐arc basin. The stable stress condition in the accretionary prism is interpreted to have resulted from mechanical decoupling by the accommodation of large displacement along the megasplay fault.

Discrete element modelling study of force distribution in a 3D pile of spherical particles

We present a numerical analysis of the transmission of contact forces in a granular pile comprising 50,000 frictional, coarse spherical particles. The goal of our study is to understand the microscopic origins of macroscopic behaviours, such as the pressure dip at the centre of the base of a conical pile. The particles are 8.2mm in diameter with a standard deviation of 0.1mm to avoid ordering effects. The effects of the pouring method, inter-particle sliding friction and rolling friction on the distribution of static stress are examined. The analysed microscopic variables are the distributions of the values and directions of the contact forces as well as the degree of mobilisation of contact friction. The vertical, radial and shear stress components are derived from the discrete contact forces. The analysed macroscopic variables are the distribution of the stress components, mobilisation of internal friction and inclination of the major principal stress to the vertical. The simulation results show that certain combinations of the examined factors lead to the formation of dome-shaped structures of maximum values of mean pressure as determined by the stress distribution inside the pile as well as at its base.

Poroelasticity During Fluid Injection in Confined Geological Reservoirs: Incorporating Effects of Seal-Rock Stiffness

SummaryThis paper presents a new poroelastic solution to describe the time-dependent response of a confined geological reservoir to fluid injection through a fully penetrating vertical well treated as a point source. Unlike previous studies, vertical-confinement effects of seal rocks are incorporated in the solution. To facilitate analytical description of a fully coupled poroelastic behavior within the reservoir, the stiffness of surrounding rocks is described by the Winkler model, simplifying the response of seal rocks in the direction perpendicular to the reservoir plane. Analytical expressions are obtained for axisymmetric stress and strain components in the reservoir and for the vertical reaction stress. The latter is essential for evaluation of integrity of seal rocks during injection. Solutions are also obtained for the magnitude and location of the maximum-induced radial displacement as a function of time during injection.The effects of poroelastic coupling are articulated through the equivalent diffusion constant of the reservoir-seal rocks system. The latter is expressed through traditional poroelastic parameters as well as the relative stiffness of reservoir and seal rocks. The Winkler modulus of seal rocks, which is involved in all analytical relationships presented in this paper, is empirically linked to elastic characteristics of surrounding strata by comparing their response with the same pressure change in the reservoir according to the ideally elastic and Winkler models.The derived solutions are compared with previous studies, and verified against fully coupled numerical simulations. A comprehensive sensitivity analysis is conducted to assess the effects of the stiffness of the confining strata on the response of a uniform reservoir to injection. The vertical component of stress and the radial and vertical displacements are found to be substantially sensitive to the magnitude of the vertical restraint. The findings note the significance of incorporating seal-rock characteristics to attain a realistic assessment of the geomechanics of injection, specifically in formations with lower elastic moduli.

Model for estimation of stress field in the earth's crust

Stress field or in-situ stress, beside rock mass strength, determines stability or instability of underground openings. It plays key role of every rock engineering project, and has been subject of many researches. There are many theoretical models of the stress field of the Earth's crust which have more or less limited domain of applicability. However, those models usually express horizontal stresses as ratio with vertical stress component. On the other side, it is well known that deformation modulus of the rock mass is dependent on the lateral stress it is subjected to. This dependence is, herein, coupled with practical findings of the stress field behavior and incorporated into the stress filed model. As the result new formulation for the stress filed components is obtained.

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.

Relation between Raman frequency and triaxial stress in Si for surface and cross-sectional experiments in microelectronics components

This paper provides a detailed description explaining how to calculate the relation between the silicon Raman frequency and local stress or strain in the silicon, applied to stress measurements in microelectronics. This relation is well known for measurements from the (100) surface of silicon. However, it is often used in the wrong way, neglecting non-zero stress tensor elements. Especially, in current 3D microelectronics technology, where the stress caused by through Si vias or micro-bumps is of large importance, the vertical stress component, which highly affects the measured Raman frequency shift, is often erroneously neglected. In addition, the equations for the (100) surface are also often used incorrectly for cross-sectional measurements from a (110) surface. In this paper, different ways to calculate the relation between Raman frequency and triaxial stress, and the related Raman peak intensities, are discussed in detail.