Effective Stress Parameter Research Articles

Concerning the fictitious continuum in damage mechanics

Consistent theories to describe damage processes are generally presented within the framework of effective stress and internal parameters. It is well known that damage is concerned with the progressive deterioration of elastic properties due to microscopic defects, such microvoids or microcracks. In the framework of Continuum Mechanics, damage is related to irreversible changes (on the microlevel) of small vicinities surrounding material points in the body. So a convenient definition of these small vicinities, named “representative material element”, will be recalled in Part 1, and application will be made to elastoplasticity in Part 2. In the subsequent parts, a fictitious suitable undamaged elastoplastic body accompanying the real damaged one is introduced in order to define the effective stress in the framework of large strains and its use in the construction of damaged elasticity law. Finally application is made to infinitesimal strains that concern most of the examples in literature. Due to limitation of place, plasticity coupled with damage is not considered in this paper.

Spectral Shear-Wave Ground-Motion Scaling in Switzerland

Three-component recordings of local and regional earthquakes and explosions are used to assess the spectral characteristics of attenuation, excitation, and duration of ground motion in Switzerland. The data set consists of 292 events in the magnitude range from 2.0 to 5.2, with a total of 2958 waveforms recorded in Switzerland and the German border region from 1984 to 2000. Distance ranges from 5 to 350 km. Stations are located on National Earthquake Hazard Reduction Program 1994 site classes A and B outcrops. Empirical excitation, site, and attenuation terms are derived for the Fourier spectra and peak ground velocities of the ground motion in the frequency range 1-15 Hz by applying an iterative damped least-squares regression. These results are used to calibrate effective theoretical attenuation and excitation models. A grid search through the parameter space is then applied to obtain the quality factor Q ( f ) and a piecewise linear geometrical spreading function G ( r ), allowing complex behavior of attenuation. Optimum results are obtained for Q ( f ) = 270 f 0.50, G ( r ) = r -1.1 for 0-50 km, r -0.6 for 50-70 km, r +0.2 for 70-100 km, and r -0.5 for distances greater than 100 km. The increased amplitudes in the distance range 70-100 km can be explained by the reflection of shear waves at the Moho. This reflected wave energy also leads to an increased duration of ground motion for the same range. The inverted excitation terms are modeled, based on Brune's source spectrum, applying an effective stress parameter of 5-10 bars and a high-frequency roll off (e- πκ fk) κ = 0.015. The small values of κ agree with the mean site condition. A regional site difference between the Alps and the Alpine Foreland site is obtained with a factor of two higher amplitudes in the latter. Manuscript received 25 August 2001.

An effective stress based numerical model for hydro-mechanical analysis in unsaturated porous media

A fully coupled flow-deformation model is presented for the behaviour of unsaturated porous media. The governing equations are derived based on the equations of equilibrium, effective stress concept, Darcy's law, Henry's law, and the conservation of fluid mass. Macroscopic coupling between the flow and deformation fields is established through the effective stress parameters. The microscopic link between the volumetric deformations of the two pore system (i.e. the pore-air and the pore-water) is established using Betti's reciprocal theorem. Both links are essential for a proper modelling of flow and deformation in unsaturated porous media. The discretised form of the governing equations is obtained using the finite element technique. As application of the model, experimental results from several laboratory tests reported in the literature are modelled numerically. Good agreement is obtained between the numerical and the experimental results in all cases.

A unique relationship for χ for the determination of the shear strength of unsaturated soils

In this note, a unique relationship between the effective stress parameter chi and the ratio of suction over the air entry value (suction ratio) is proposed, based on the shear strength data reported in the literature. Comparisons are made between the measured and the calculated shear strengths for two laboratory prepared unsaturated soils. Extremely good agreement has been obtained between the measured and the calculated values using the proposed relationship. (A)

Numerical Analysis of Drained Direct and Simple Shear Tests

The authors present an interesting study on direct shear testing. The discusser estimates that practicing engineers perform laboratory direct shear tests 80-90% of the time. The remainder is mostly laboratory compression tests, such as unconfined compression or triaxial compression. The reason direct shear tests are used so often in practice is because they are quick to set up, simple to run, and the results are easy to interpret. Because the direct shear is used so often, it is frequently considered to be the standard of practice. The direct shear test is typically used to determine the effective stress parameters (ASTM 0 3080-72: Direct 1986), by first consolidating the soil sample and then shearing it slow enough to enable the dissipation of shear-induced excess pore pressure. Inaccurate results are common for clayey soil because they are not consolidated prior to shearing or sheared too quickly. The authors performed a theoretical analysis and have concluded that in most cases, direct shear tests overestimate the peak shear strength by as much as 7.5%. This translates into an increase in effective friction angle up to 2°. The unconservative nature of the direct shear test is one of it's main disadvantages. The discusser was wondering what conditions cause the direct shear test to have the highest overestimate (7.5 %) of peak shear strength? What soil type would this correspond to?

Scatter characteristics of fatigue life in normalized 0.21% carbon steel plain specimens: Goto, M., Nisitani, H. and Yakushiji, T. J Soc Mater Sci Jpn (Feb. 1993) 42 (473), 163–168 (in Japanese)

This paper presents a comprehensive investigation into non-proportional multi-axial fatigue of welded components by introducing an equivalent structural stress parameter that takes into account of load-path non-proportionality in addition to plate thickness and stress state effects. This is accomplished by formulating a “moment of load path” or “MLP” based fatigue damage parameter that provides a consistent treatment of load-path non-proportionality under arbitrary multi-axial loading conditions for which cycle counting can be consistently performed by means of a previously developed path-dependent maximum range (PDMR) cycle counting procedure. To examine its broad applicability and effectiveness, non-proportional multi-axial test data obtained using different components, joint types, and loading conditions from various sources are analyzed using the newly developed equivalent stress parameter. The results show that the new equivalent stress parameter enables not only an effective consolidation of all multi-axial test data (up to about 300 tests) analyzed in this paper into a narrow band, but also the demonstrated transferability between the master S-N curve (dominated by test data under uniaxial cyclic loading conditions) adopted by the 2007 ASME Div 2 and API 579 RP/ASME FFS-1 Codes and the consolidated S-N curve dominated by severe non-proportional multi-axial cyclic loading conditions. As a result of the present development, a unified fatigue evaluation procedure based on the newly proposed effective stress parameter and a single master S-N curve can be implemented for arbitrary cyclic loading conditions regardless of stress multi-axiality or load path proportionality.

Effect of non-proportional loading on creep-fatigue properties of 304 stainless steel at low strain ranges near the elastic region: Asayaman, T., Aoto, K. and Wada, Y. Nucl Eng Des (Mar. 1993) 139 (3), 299–309

This paper presents a comprehensive investigation into non-proportional multi-axial fatigue of welded components by introducing an equivalent structural stress parameter that takes into account of load-path non-proportionality in addition to plate thickness and stress state effects. This is accomplished by formulating a “moment of load path” or “MLP” based fatigue damage parameter that provides a consistent treatment of load-path non-proportionality under arbitrary multi-axial loading conditions for which cycle counting can be consistently performed by means of a previously developed path-dependent maximum range (PDMR) cycle counting procedure. To examine its broad applicability and effectiveness, non-proportional multi-axial test data obtained using different components, joint types, and loading conditions from various sources are analyzed using the newly developed equivalent stress parameter. The results show that the new equivalent stress parameter enables not only an effective consolidation of all multi-axial test data (up to about 300 tests) analyzed in this paper into a narrow band, but also the demonstrated transferability between the master S-N curve (dominated by test data under uniaxial cyclic loading conditions) adopted by the 2007 ASME Div 2 and API 579 RP/ASME FFS-1 Codes and the consolidated S-N curve dominated by severe non-proportional multi-axial cyclic loading conditions. As a result of the present development, a unified fatigue evaluation procedure based on the newly proposed effective stress parameter and a single master S-N curve can be implemented for arbitrary cyclic loading conditions regardless of stress multi-axiality or load path proportionality.

Effective stress vane shear strength correction factor correlations

A recent effective stress model of vane shear strength testing in soils can relate measured torques to vane shear strengths using theoretical analysis in terms of effective stress parameters. The strength estimates are based on known in situ stresses and soil parameters derived from laboratory testing. The model may be applied, for example, in obtaining theoretical estimates of conventional undrained vane shear strengths for comparison with field data and for use in stability analyses. However, the model incorporates a correction factor μv, analogous to Bjerrum's field vane shear strength correction factor μ, intended to compensate for pore-pressure and shearing-rate effects. This correction factor must be evaluated before reliable torque or shear strength estimates can be made in any given case. To facilitate this, the paper presents correlations of μv with both liquid limit and plasticity index, based on world-wide data from clays and silts. The correlations are compared with independent data from Norwegian clays. Key words : clay, correction factor, effective stress, liquid limit, plasticity index, silt, vane shear strength.

Fatigue behaviour of welded joints in offshore steel structures. III. Fracture mechanics: Scholte, H. G. EUR Rep. 13395 1992 270 pp

Modeling of vibration fatigue of welded structures in the frequency domain can be particularly challenging. For instance, the stress singularity at weld locations causes finite element size sensitivity in stress determination. Furthermore, the interactions of multiple vibration modes at a weld location can generate non-proportional multiaxial stresses. Here we present a comprehensive procedure for modeling multiaxial fatigue behaviors of welded structures in the frequency domain to address some of these issues. The procedure utilizes a robust mesh-insensitive method and modal decomposition approach to determine the normal and shear traction stress responses. We proposed a non-proportionality correlation function to interrelate the resulting power spectrum density (PSD) of normal and shear traction stresses and their cross-PSD (CPSD) for establishing an effective stress parameter. The correlation function is determined and validated based on the well-established time-domain path-dependent maximum range (PDMR) method through a small-scale data-driven approach.

Fatigue characteristics of work roll in roughing stands of hot strip mill: Lee, W. H., Kim, S.J., Son, B.H., Lee, Y.H., Yi, J.J. and Kim, J.K. Research Institute of Industrial Science and Technology (Pohang City) Technical Research Report5 4 (Dec 1991) 822–832 (in Korean)

This paper presents a comprehensive investigation into non-proportional multi-axial fatigue of welded components by introducing an equivalent structural stress parameter that takes into account of load-path non-proportionality in addition to plate thickness and stress state effects. This is accomplished by formulating a “moment of load path” or “MLP” based fatigue damage parameter that provides a consistent treatment of load-path non-proportionality under arbitrary multi-axial loading conditions for which cycle counting can be consistently performed by means of a previously developed path-dependent maximum range (PDMR) cycle counting procedure. To examine its broad applicability and effectiveness, non-proportional multi-axial test data obtained using different components, joint types, and loading conditions from various sources are analyzed using the newly developed equivalent stress parameter. The results show that the new equivalent stress parameter enables not only an effective consolidation of all multi-axial test data (up to about 300 tests) analyzed in this paper into a narrow band, but also the demonstrated transferability between the master S-N curve (dominated by test data under uniaxial cyclic loading conditions) adopted by the 2007 ASME Div 2 and API 579 RP/ASME FFS-1 Codes and the consolidated S-N curve dominated by severe non-proportional multi-axial cyclic loading conditions. As a result of the present development, a unified fatigue evaluation procedure based on the newly proposed effective stress parameter and a single master S-N curve can be implemented for arbitrary cyclic loading conditions regardless of stress multi-axiality or load path proportionality.

Modification of the bree diagram in presence of primary transient loads

The design of Class 1 LMFBR components operating at elevated temperature is accomplished in accordance with ASME III and Code Case N-47-28. The main problem encountered in the design of components at elevated temperature is the satisfaction of strain limits according to the requirements of Test No. B-1, in the presence of significant seismic loads with very short duration ( <40 s ). These transient primary loads in Test No. B-1 are treated like steady primary loads, and very often Test No. B-1 is not passed, causing more complex analyses to be performed for component strain limits satisfaction. New formulae for calculating the residual stress distribution in the elastic core (core stress) and the effective creep stress parameter Z have been proposed to take into account the transient nature of seismic loads. A comparison between results obtained in calculating Z according to Test No. B-1 or using the new formulae is presented in this paper; the new method for Z calculation appears to be more accurate and to give less conservative results than previous approaches.

Biaxial Low Cycle Fatigue of Unaged and Aged 1Cr-1Mo-1/4V Steels at Elevated Temperature

This paper describes the biaxial low cycle fatigue of unaged and aged 1Cr-1Mo-1/4V rotor steels at 823 K in air. Combined push-pull and reversed torsion tests were carried out on these steels and the biaxial fatigue data were obtained. Aging significantly reduced the hardness of the steel but had no effect on the crack direction in biaxial low cycle fatigue. Aging also had no effect on the data correlation using the biaxial strain parameters, but had a significant effect on the data correlation using the biaxial stress parameters. The change in the effective stress parameter in correlating the biaxial fatigue data due to aging is discussed in connection with the material softening.

Comparison of finite element and limiting equilibrium analyses for an embedded cantilever retaining wall

The design of embedded cantilever retaining walls is often based on approximate limit equilibrium calculations. In this Paper the results of a limit equilibrium approach are compared with the results of a finite element study. Predictions of both embedment depth and maximum bending moments are compared and the finite element study is used to show the influence of such parameters as initial soil stress conditions and construction procedure. For the finite element study an elasto-plastic constitutive law is used to model the soil behaviour. The soil is assumed to behave in a fully drained manner with zero pore fluid pressures everywhere. Effective stress parameters are used to define the soil strength. The results of the comparison indicate that both the limit equilibrium method used in the Paper and the finite element approach give similar predictions of the embedment depth required to ensure stability. The maximum bending moment was calculated using two different limit equilibrium approaches. Generally it was found that predictions based on these approaches were greater than the corresponding values from the finite element analyses. In particular, for embedded cantilever walls formed by excavation in low K0 soils or by bachtIlling one of the limit equilibrium approaches provided an overestimate of almost 50% of the maximum bending moment value predicted by the finite element method at a factor of safety of 2. The results of the study indicate that some reduction in bending moment as calculated by the limit equilibrium method may therefore be warranted. La construction des murs de soutènement cantilever encastrés se base souvent sur des calculs approximatifs de I'équlibre limite. L'article compare les résultats obtenus à partir de l'équilibre limite avec ceux d'une étude à éléments finis. Des prédictions de la profondeur de l'encastrement et des moments de flexion maximaux sont comparées et l'étude à éléments finis eat utilisée afin de démontrer l'influence de certains paramètres, telsque les conditions initiales de la contrainte du sol et la méthode de construction. Dans le cas de I'étude à éléments finis une loi constitutive élasto-plastique s'emploie pour modeler le comportement du sol. On admet que le sol se comporte d'une manière pleinement drainée avec des pressions interstitielles des fluides qui sont nulles partout. La résistance du sol est définie à partir des paramètres de contrainte effective. Les résultats de la comparaison indiquent que des prédictions semblables de la profondeur d'encastrement, nécessaire pour garantir la stabilité sont données tant par la méthode d'équilibre limite décrite dans l'article que par la méthode à éléments finis. Le moment de flexion maximal a été calculé à I'aide de deux méthodes différentes d'équilibre limite. On trouve qu'en général la prédictions basées sur ces méthodes sont plus élevées que lea valeurs correspondantes obtenues à partir des analyses à éléments finis. Notamment pour les mnrs de soutènement cantilever encastrés formés par I'excavation dans des sols à K0 réduit et par remblayage I'une des methodes d'équilibre limite fournit une surévaluation de presque 50% de la valeur maximale du moment de flexion predite par la méthode à éléments finis avec un facteur de sécurité 2. Les résultats de l'étude indiquent qu'une certaine réduction du moment de flexion calculé par la méthode d'équilibre limite peut alors être justifrée.

Bearing capacity of friction piles in marine clay

A full-scale investigation with two instrumented test piles was carried out at the St Alban test site, to study the increase in bearing capacity with time of short friction piles jacked into an over-consolidated soft sensitive marine clay. It is shown that the increase in shaft bearing capacity with time is significant and reaches about 12 times the initial shaft supporting capacity. The maximum skin friction is developed when the excess pore pressures generated during driving are fully dissipated after about 600 h. The results of load tests strongly suggest that effective stress parameters govern the behaviour of friction piles during the reconsolidation phase. The shaft bearing capacity is underestimated by approximately 45% with an effective stress approach in which the Ko, value is inferred from 1 – sin φ. However, if the measured values of Ko are taken, the calculated load carried by shaft friction is 70–90% of the actual shaft capacity. It is shown that the ultimate toe bearing capacity is strain rate dependent. For strain rates less than 5 × 10-4/s, which corresponds to pile penetration rates less than O·1 cm/s, the behaviour of tbe clay surrounding the toe is partially drained. Thus, the prediction of toe resistance for load testing conditions, i.e. a penetration rate of about 0·0001 cm/s, is complex and cannot be carried out with the undrained characteristics of the clay. Un essai en vraie grandeur a été effectué sur deux pieux instrumentés au centre d'expéiences de St Alban afin d'étudier I'accroissement dans le temps de la portance des pieux flottants courts vérinés dans une argile marine tendre surconsolidée sensible au remaniement. L'article démontre que la portance s'accroît de façon significative dans le temps et atteint environ 12 fois la valeur originale. Le frottement maximal est atteint lorsque les surpressions interstitielles créées au cours du battage des pieux se dissipent complètement après environ 600 h. Les résultats des essais de chargement montrent que les paramètres de contrainte effective régissent le comportement des pieux flottants pendant la phase de reconsolidation. La portance est sous-estimée d'environ 45% avec une méthode employant la contrainte effective dans laquelle la valeur Ko, est prise égale à 1 – sin ø. Cependant, si on prend les valeurs mesurées de Ko la charge calculée portée par le frottement représente entre 70% et 90% de la capacité réelle. On démontre que la force portance limite de pointe dépend dutaux de déformation. Pour des taux de déformation inférieurs à 5 × 10-4'/s, ce qui correspond à des vitesses de pénétration inférieures à 0, l cm/s, le comportement de l'argile entourant la base du pieu est partiellement drainé Il est ainsi très dificile de prédire la réistance de pointe pour des conditions d'essais de chargement, c'est-à-dire un taux de pénétration d'environ 0,001 cm/s, et aucune prédiction ne peut se faire sur la base des caractéristiques non-drainées de l'argile.

Book reviews BromheadE. N.The Stability of SlopesSurrey University PressLondon1986£40.00373

The introduction to this useful book starts by discussing classifications of falls, slide and flows, going on to a brief history, mentioning important historical personalities and events, such as Collin, Hutton Gregory, Gothernburg harbour quay wall and Fort Peck dam failures and the roles of Terzaghi and Skempton. Chapter 2, discussing natural slope failures, contains a notable series of drawings, photographs and analyses of various kinds of slides, including such classics as Herne Bay cliffs, South Wales valley landslides and the Black Venn mudslides. Fundamental properties of soils and rocks are discussed in Chapter 3, where concepts of effective stress and of residual strength are introduced and the importance of discontinuities discussed. In Chapter 4, discussion on measurement of shear strength, ring shear testing is emphasized; other methods of testing are also discussed. Principles of stability analysis (Chapter 5) begins with a consideration of the φ = 0 (total stress) method of analysis, although the author has previously (p. 71) mentioned the difficulties and limitations of this method; the bulk of the discussion is about various methods using effective stress parameters. The discussion continues in Chapter 6 where the use of computers, with detailed examples, and stability charts is discussed. Detailed consideration is given in Chapter 7 to seepage and pore water pressures where examples are, among others, taken from Cow Green, Balderhead and Tarbela dams, as well as natural slopes at Herne Bay and the Isle of Sheppey. Chapter 8 concentrates on remedial measures, including ground anchors, drainage (both

Influence of the back pressure technique on the shear strength of soils. Technical note : Allam, M M; Sridharan, A Geotech Test J, V3, N1, March 1980, P35–40

A series of consolidated-undrained triaxial tests with pore pressure measurement were carried out to study the influence of the back pressure technique on the shear strength of soils. Hand-remolded samples of normally consolidated and overconsolidated kaolinite, compacted samples of kaolinite, hand-remolded normally consolidated black cotton soil, and hand-remolded and undisturbed samples of red earth were tested with and without the back pressure technique. The results indicate that a back pressure can significantly influence the shear strength and pore pressure response of soils. Two mechanisms govern the influence of the back pressure; which one applies depends on whether the soils compress or dilate during shear. The effective stress parameters are essentially unaffected by the back pressure technique. A partial consolidation technique promises to be an effective time-saving method of determining the shear strength parameters. (Author)

Shear Strength Behaviour of Overconsolidated Clays

It is generally understood that there exists a hysteresis loop between the normally consolidated and overconsolidated effective stress Mohr-Coulomb-failure envelopes, the size of hysteresis loop being a function of the past maximum consolidation pressure. Research findings of different investigators in this regard are at variance. This paper presents the results of an experimental investigation on two remoulded clays in CIU compression tests, varying both maximum past consolidation pressure and the overconsolidation ratio. Test data is analysed in terms of Mohr-Coulomb as well as Hvorslev failure envelopes. Test results show that the effective stress Mohr-Coulomb failure envelopes are uniquely defined independent of overconsolidation ratio, past maximum pressure and the failure condition such as the peak deviator stress, peak effective principal stress ratio and the peak porewater pressure. When the failure is denfined at a strain level lower than that of the peak stress condition, unique effective stress parameters ( c ' and ϕ ') equal to the peak stress values are observed at pre-peak strains (ε ≃ 6 percent) even bofore the peak stress conditions are reached (ε a ≃ 15 percent). From the view point of Hvorslev criterion, the shear strength of the two remoulded soils is essentially through ϕ e ' and it is independent of maximum past pressure.

Stress path effects on the strength behaviour of a layered soil

An experimental investigation dealing with the influence of stress path on the shear behaviour of a layered soil prepared in the laboratory is described. Specimens trimmed in vertical and horizontal directions have been sheared under three different stress paths in compression and extension tests. Either in compression or extension, the stress–strain behaviour of the specimens with both orientations was apparently the same, although the volume change behaviour was different. The effective stress parameters C′ and [Formula: see text]′ were found to be unique and independent of the stress path and two principal orientations. However, the values of [Formula: see text]′ in extension tests were 6–7° higher than those in compression tests.

Influence of the Back Pressure Technique on the Shear Strength of Soils

Abstract A series of consolidated-undrained triaxial tests with pore pressure measurement were carried out to study the influence of the back pressure technique on the shear strength of soils. Hand-remolded samples of normally consolidated and overconsolidated kaolinite, compacted samples of kaolinite, hand-remolded normally consolidated black cotton soil, and hand-remolded and undisturbed samples of red earth were tested with and without the back pressure technique. The results indicate that a back pressure can significantly influence the shear strength and pore pressure response of soils. Two mechanisms govern the influence of the back pressure; which one applies depends on whether the soils compress or dilate during shear. The effective stress parameters are essentially unaffected by the back pressure technique. A partial consolidation technique promises to be an effective time-saving method of determining the shear strength parameters.

The quick-clay slide at Baastad, Norway, 1974

The Baastad landslide occurred within a large area of marine clay deposits where the clay had been transformed into quick clay from leaching. The landscape in the area is highly dissected from stream erosion and numerous slope failures and slides. The slide scar covers about 80,000 m 2 of farmland. Three buildings were destroyed in the slide. According to observations and investigations, the whole area slid out almost simultaneously, i.e., the slide was of the so-called flake type. For all known documented slides of this category, conventional stability analysis based on ultimate effective stress parameters φ′ and c′, give values of the factor of safety which are too high. It is an unsafe procedure. The behaviour of quick-clays has been studied extensively at the Norwegian Geotechnical Institute over the last 20 years. These studies show that the strength properties of these clays should be based on undrained shear strength values rather than the parameters φ′ and c′. Back calculations of the Baastad slide based on undrained shear strength values have been carried out and were in good agreement with the theoretical value of the factor of safety.