Isotropic Stress Conditions Research Articles

The use of a particle method for the modelling of isotropic membrane stress for the form finding of shell structures

The best known isotropic membrane stress state is a soap film. However, if we allow the value of the isotropic stress to vary from point to point then the surface can carry gravity loads, either as a hanging form in tension, or as a masonry shell in compression. The paper describes the theory of isotropic membrane stress under gravity load and introduces a particle method for its numerical simulation for the form finding of shell structures.

A finite strain closed‐form solution for the elastoplastic ground response curve in tunnelling

SUMMARYThe ground response to tunnel excavation is usually described in terms of the characteristic line of the ground (also called ‘ground response curve’, GRC), which relates the support pressure to the displacement of the tunnel wall. Under heavily squeezing conditions, very large convergences may take place, sometimes exceeding 10–20% of the excavated tunnel radius, whereas most of the existing formulations for the GRC are based on the infinitesimal deformation theory. This paper presents an exact closed‐form analytical solution for the ground response around cylindrical and spherical openings unloaded from isotropic and uniform stress states, incorporating finite deformations and linearly elastic‐perfectly plastic rock behaviour obeying the Mohr–Coulomb failure criterion with a non‐associated flow rule. Additionally, the influence of out‐of‐plane stress in the case of cylindrical cavities under plane‐strain conditions is examined. The solution is presented in the form of dimensionless design charts covering the practically relevant parameter range. Finally, an application example is included with reference to a section of the Gotthard Base tunnel crossing heavily squeezing ground. The expressions derived can be used for preliminary convergence assessments and as valuable benchmarks for finite strain numerical analyses. Copyright © 2014 John Wiley & Sons, Ltd.

Characterization of gas flow through low-permeability claystone: laboratory experiments and two-phase flow analyses

Abstract For the characterization of gas migration through a low-permeability clay host rock for deep underground repositories, a comprehensive understanding of the relevant phenomena of gas and fluid flow through low-permeability clay is required. The National Cooperative for the Disposal of Radioactive Waste (Nagra) in Switzerland has developed a comprehensive programme to characterize gas flow in low-permeability Opalinus Clay through laboratory tests and detailed numerical analyses for developing appropriate constitutive models. Laboratory tests were performed on cores by two different laboratories, the Laboratory for Soil Mechanics at EPFL and the Department of Geotechnical Engineering and Geosciences at UPC. Loading tests were performed by both laboratories to study rock compressibility at different stress levels and water permeability dependence on void ratio. The water retention behaviour demonstrated by EPFL and UPC produced comparable results. Water permeability tests and fast controlled-volume air injection experiments were performed in a triaxial cell under isotropic stress conditions on two samples with flow parallel and normal to the bedding planes. A confining stress of 15 MPa was applied during gas testing, corresponding to a lithostatic pressure at a depth of c. 600 m below ground. For detailed analyses, the two-phase flow code TOUGH2 ( Pruess et al. 1999 ) was used. This considers fluid flow in both liquid and gas phases under the influence of pressure, viscous and gravity forces, according to Darcy's law. The standard analyses could not reproduce the measured pressure responses well, and the calibrated hydraulic and two-phase parameters were not consistent with the preceding water test and laboratory analyses. Implementing the non-linear behaviour in terms of the observed relationship between changes in void ratio and associated changes in permeability under different stress conditions significantly improved the simulated results, resulting in a conceptual model that well reproduced the observed injection pressure and outflow responses for both tests, parallel and normal to bedding, using a consistent parameter set.

Uniqueness and existence in plasticity models for unsaturated soils

The paper investigates the mathematical structure of plasticity models for unsaturated soils and provides a strategy to capture the loss of uniqueness of the incremental solution upon loading and/or wetting paths. To derive bifurcation conditions in simple analytical form, the analysis is restricted to isotropic stress states. This choice has allowed the inspection of the most common classes of constitutive models through a unified notation, as well as the study of different forms of coupling between plasticity and state of saturation. It is shown that, similar to saturated soil plasticity, the loss of admissibility of the plastic solution is governed by critical values of the hardening modulus. At variance with the classical case, however, these moduli can be positive even if the plastic flow rule is associated (bifurcation in the hardening regime). The paper shows that such non-trivial features derive from hydro-mechanical coupling, i.e. they depend on the approach used to reproduce suction effects and evolving retention properties. In other words, although the problem of loss of uniqueness affects all classes of plasticity models for unsaturated soils, different constitutive assumptions may not have the same outcome in terms of bifurcation potential. As a result, new concepts are introduced to compare the mathematical robustness of the different constitutive approaches, as well as to interpret their predictions in the light of precise bifurcation criteria.

Statically and Dynamically Measured Poisson's Ratio of Granular Soils on Triaxial Laboratory Specimens

Poisson's ratios and small-strain stiffnesses of three kinds of granular materials—fine, medium coarse, and coarse sands—were evaluated in the laboratory. Both axial and radial strains of cylindrical triaxial specimens were measured with a local deformation transducer and clip gauges. Small-strain (≈0.001 %) cyclic loadings were applied in the vertical direction at several isotropic stress states. We determined Poisson's ratio statically based on the local strain variations during the cyclic loadings; we also investigated the stiffness in parallel. In conjunction with static measurements, elastic waves were propagated. By utilizing the disk transducer method, we were able to measure both compressional and shear waves in a single specimen under identical stress states. Based on the received wave velocities of compressional and shear waves, we were able to evaluate both Poisson's ratio and the small-strain stiffness dynamically. We then compared elastic parameters evaluated both statically and dynamically for the geo-materials.

Hydro-mechanical hypoplastic models for unsaturated soils under isotropic stress conditions

The current work presents two hypoplastic models to predict the hydraulic and mechanical behavior of the unsaturated soils. The hydraulic model is capable to reproduce the observed hysteretic behavior for the drying and wetting processes and incorporates the void ratio dependence. The mechanical model is written in terms of the Bishop effective stress and is limited only to isotropic states. It incorporates a normal consolidation line that depends on the degree of saturation. Both models were developed under the hypoplastic framework and therefore are capable to simulate the observed behavior without defining a yield surface. Simulations of some experiments performed with Pearl clay suggest that the models accurately predict its hydro-mechanical behavior.

Formulation of a three‐dimensional constitutive model for unsaturated soils incorporating mechanical–water retention couplings

SUMMARYWheeler, Sharma and Buisson proposed an elasto‐plastic constitutive model for unsaturated soils that couples the mechanical and water retention behaviours. The model was formulated for isotropic stress states and adopts the mean Bishop's stress and modified suction as stress state variables. This paper deals with the extension of this constitutive model to general three‐dimensional stress conditions, proposing the generalized stress–strain relationships required for the numerical integration of the constitutive model. A characteristic of the original model is the consideration of a number of elasto‐plastic mechanisms to describe the complex behaviour of unsaturated soils. This work presents the three‐dimensional formulation of these coupled irreversible mechanisms in a generalized way including anisotropic loading. The paper also compares the results from the model with published experiments performed under different loading conditions. The response of the model is very satisfactory in terms of both mechanical and water retention behaviours. Copyright © 2013 John Wiley & Sons, Ltd.

Experimental study of asphaltic concrete dynamic properties as an impervious core in embankment dams

The seismic behaviour of asphaltic concrete used as an impervious core in embankment dams was investigated.To evaluate the specimen’s dynamic behaviour, an extensive series of monotonic and cyclic triaxial tests were carried out. Bitumen content between 5.5% and 7.0% with 0.5% increments were selected for the tests. Isotropic and anisotropic initial stress conditions with different principal stress ratio were also considered in this study. Thousands of cycles were imposed on some of the specimens, to study their fatigue behaviour due to seismic loading. A small degradation could be seen but no cracking was observed on the cutting surfaces. All tests were carried out at a constant temperature of 22°C simulating a constant temperature inside a dam in tropical climate regions. Shear modulus in the compression region (Gc) and tension region (Ge) are presented for different Bitumen content, confining stress, stress ratio (Kc) and loading type. The damping ratio was also presented for different loading states. A regression equation was also derived for determining cyclic and maximum shear modulus (Gmax) of the asphaltic concrete for different Bitumen content as a function of confining stress which can be used in numerical studies.

Measuring ultrasonic characterisation to determine the impact of TOC and the stress field on shale gas anisotropy

While the majority of natural gas is produced from conventional sources, there is significant growth from unconventional sources, including shale-gas reservoirs. To produce gas economically, candidate shale typically requires a range of characteristics, including a relatively high total organic carbon (TOC) content, and it must be gas mature. Mechanical and dynamic elastic properties are also important shale characteristics that are not well understood as there have been a limited number of investigations of well-preserved samples. In this study, the elastic properties of shale samples are determined by measuring wave velocities. An array of ultrasonic transducers are used to measure five independent wave velocities, which are used to calculate the elastic properties of the shale. The results indicated that for the shale examined in this research, P- and S-wave velocities vary depending on the isotropic stress conditions with respect to the fabric and TOC content. It was shown that the isotropic stress significantly impacts velocity. In addition, S-wave anisotropy was significantly affected by increasing stress anisotropy. Stress orientation, with respect to fabric orientation, was found to be an important influence on the degree of anisotropy of the dynamic elastic properties in the shale. Furthermore, the relationship between acoustic impedance (AI) and TOC was established for all the samples.

On the undrained strain-induced anisotropy of loose sand

An experimental study was carried out to investigate the effects of previous deviatoric strain histories on the undrained behaviour of loose and saturated Toyoura sand and compared with known results of Hostun RF sand. From an initial isotropic stress state, recent deviatoric strain histories in the compression side of the triaxial plane were generated by a standard drained presheared cycle up to a specified mobilized stress ratio. Mainly, the fully liquefied, contractive, unstable and softening behaviour of loose sand was progressively transformed into the non-liquefied, dilative, fully stable and hardening behaviour of dense-like sand, while remaining within a narrow range of loose density. The paper validates and extends the current understanding of strain-induced anisotropy of loose sand. New experimental data support the directional dependency of the instability cone on the stress increment direction, suggest the bifurcation characteristics of loose sand and evidence the important role of past deviatoric strain histories.

Probing into the strain induced anisotropy of Hostun RF loose sand

Several recent linear drained preloading histories with fixed direction were especially designed to study the effects of strain induced anisotropy of loose Hostun RF sand in the compression side of the classical triaxial plane. Nearly identical void ratio and a same initial isotropic stress state prior to the final undrained shearing in compression are the requirements of the experimental program to take into account only the deviatoric strain histories. The effects of previous deviatoric strain histories on the undrained response of loose Hostun RF sand are identified: mainly the progressive transformation of a contractive and unstable behaviour of very loose sand into a dilative and stable behaviour of dense-like sand by previous linear drained history, while remaining in the same state of loose density. Experimental data evidence the directional dependency of the initial gradient of the effective stress paths, independent of the length of the approaching linear stress paths; the large common non linear effective stress response up to the deviatoric stress peak; the progressive appearance of the dilatancy domain and the unexpected evolution of the undrained behaviour of loose and presheared sand. The paper provides new insights into the mechanisms of strain induced anisotropy of loose sand created by simple linear triaxial stress paths from an isotropic stress state.

The complexity of 3D stress-state changes during compressional tectonic inversion at the onset of orogeny

Abstract Compressional tectonic inversions are classically represented in 2D brittle failure mode (BFM) plots that illustrate the change in differential stress ( σ 1 − σ 3 ) versus the pore-fluid pressure during orogenic shortening. In these BFM plots, the tectonic switch between extension and compression occurs at a differential stress state of zero. However, mostly anisotropic conditions are present in the Earth's crust, making isotropic stress conditions highly questionable. In this study, theoretical 3D stress-state reconstructions are proposed to illustrate the complexity of triaxial stress transitions during compressional inversion of Andersonian stress regimes. These reconstructions are based on successive late burial and early tectonic quartz veins which reflect early Variscan tectonic inversion in the Rhenohercynian foreland fold-and-thrust belt (High-Ardenne Slate Belt, Belgium, Germany). This theoretical exercise predicts that, no matter the geometry of the basin or the orientation of shortening, a transitional ‘wrench’ tectonic regime should always occur between extension and compression. To date, this intermediate regime has never been observed in structures in a shortened basin affected by tectonic inversion. Our study implies that stress transitions are therefore more complex than classically represented in 2D. Ideally, a transitional ‘wrench’ regime should be implemented in BFM plots at the switch between the extensional and compressional regimes.

Computational simulation of hemodynamic-driven growth and remodeling of embryonic atrioventricular valves

Embryonic heart valves develop under continuous and demanding hemodynamic loading. The particular contributions of fluid pressure and shear tractions in valve morphogenesis are difficult to decouple experimentally. To better understand how fluid loads could direct valve formation, we developed a computational model of avian embryonic atrioventricular (AV) valve (cushion) growth and remodeling using experimentally derived parameters for the blood flow and the cushion stiffness. Through an iterative scheme, we first solved the fluid loads on the axisymmetric AV canal and cushion model geometry. We then applied the fluid loads to the cushion and integrated the evolution equations to determine the growth and remodeling. After a set time of growth, we updated the fluid domain to reflect the change in cushion geometry and resolved for the fluid forces. The rate of growth and remodeling was assumed to be a function of the difference between the current stress and an isotropic homeostatic stress state. The magnitude of the homeostatic stress modulated the rate of volume addition during the evolution. We found that the pressure distribution on the AV cushion was sufficient to generate leaflet-like elongation in the direction of flow, through inducing tissue resorption on the inflow side of cushion and expansion on the outflow side. Conversely, shear tractions minimally altered tissue volume, but regulated the remodeling of tissue near the cushion surface, particular at the leading edge. Significant shear and circumferential residual stresses developed as the cushion evolved. This model offers insight into how natural and perturbed mechanical environments may direct AV valvulogenesis and provides an initial framework on which to incorporate more mechano-biological details.

Determination of small-strain stiffness of Shanghai clay on prismatic soil specimen

Although a large number of tunnels and deep excavations have been constructed in Shanghai, small-strain stiffness properties of natural Shanghai clay have rarely been reported in the literature. In this study, the degree of inherent stiffness anisotropy of natural Shanghai clay was investigated in a triaxial apparatus equipped with local strain transducers and a shear-wave velocity measurement system. Three sets of side-mounted bender elements, consisting of one transmitter and two receivers each, were installed on a prismatic specimen. Two series of triaxial tests on prismatic specimens of intact Shanghai clay were carried out under an isotropic stress state. Shear-wave velocities and hence elastic shear moduli in different planes were determined from bender element measurements. The cross-correlation method using two received signals gives rise to the most objective and repeatable results on shear-wave velocities in comparison with other commonly used methods. Intact Shanghai clay clearly exhibits inherent stiffness anisotropy in terms of its elastic shear modulus ratio (G0(hh)/G0(hv)) of about 1.2 for a mean effective stress varying from 50 to 400 kPa. The measured higher stiffness in the horizontal plane may be attributed to the stronger layering structure in the horizontal bedding plane. A unique relationship is found that relates the normalized shear moduli to the stress state in each plane by incorporating a void ratio function in the form of F(e) = e–2.6.

Using modified state surface approach to select parameter values in the Barcelona basic model

SUMMARYThe Barcelona basic model (BBM) successfully explained many key features of unsaturated soils and received extensive acceptance. It is also one of the few elastoplastic constitutive models for unsaturated soils that have been implemented within finite element codes and applied to the analysis of real boundary value problems. The BBM was proposed in incremental forms according to theories of soil plasticity in which individual aspects of the isotropic virgin behavior are controlled by multiple parameters, whereas at the same time, a single parameter controls more than one aspect of soil behavior. Although a variety of methods have been recently developed for calibrating model parameters for elastoplastic soil models, at present, there are no well‐established, simple, and objective methods for selecting parameter values in the BBM from laboratory tests. This has been one of the major obstacles to the dissemination of this constitutive model beyond the research context.This article presents an optimization approach especially developed for simple and objective identification of material parameters in the BBM. This is achieved by combining a modified state surface approach, recently proposed to model the elastoplastic behavior of unsaturated soils under isotropic stress conditions, with the Newton or quasi‐Newton method to simultaneously determine the five parameters governing isotropic virgin behavior in the BBM. The comparison between results using the proposed method and an existing method for the same laboratory tests was discussed from which the simplicity and objectivity of the proposed method were evaluated. Copyright © 2012 John Wiley & Sons, Ltd.

Calibration of elasto-plastic models for unsaturated soils under isotropic stresses

This paper presents a new method for selecting parameter values in elasto-plastic models for unsaturated soils under isotropic stress states. The proposed method is an improvement over more traditional calibration approaches as it explicitly takes into account experimental yielding behavior when defining the unsaturated normal compression surface. This is achieved by “enriching” measured yield stresses with corresponding values of specific volume (estimated from the observed elastic and virgin responses), which generates experimental points that can be interpolated together with virgin compression data. The proposed methodology is general and independent of the chosen mathematical forms of normal compression surface, elastic law and constitutive variables. The validity of the method is demonstrated by calibrating a reference model from a set of constant suction isotropic compression tests. Both improved and traditional calibration approaches are employed to select model parameter values which are then used to predict yield curves in the mean net stress–suction plane. Because of the incorporation of yielding data in the interpolation of the normal compression surface, the improved calibration method produces a more accurate prediction of yield stresses at different suctions compared with the standard method. Due to its generality and limited subjectivity, the proposed method provides an unbiased tool to compare strengths and weaknesses of different constitutive models.

A Modified Triaxial Apparatus for Measuring the Stress Path-Dependent Water Retention Curve

Abstract This article reports a modified triaxial apparatus for measuring the stress path-dependent water retention curve (SDWRC) of unsaturated soils under isotropic and deviatoric stress conditions. In this modified triaxial apparatus, an open-ended, bottle-shaped inner cell is installed together with a differential pressure transducer to measure the total volume change of a specimen accurately for the correct determination of the degree of saturation of an SDWRC. Details of the calibration and test procedures are described and discussed. Some test results from compacted samples of a completely decomposed tuff, i.e., silt of low plasticity, are also presented in order to demonstrate the key features of the modified apparatus.

Effects of Previous Deviatoric Strain Histories on the Undrained Behaviour of Hostun RF Loose Sand

The effects of previous deviatoric strain histories on the undrained behaviour of very loose and saturated Hostun RF clean sand are investigated in this paper. From an initial isotropic stress state in the triaxial plane, strain histories are generated by isotropic consolidation followed by standard drained triaxial preshear or presheared cycle, either in compression or in extension, up to a desired value of axial strain or mobilized stress ratio. Deviatoric strain histories are achieved by having nearly the same void ratio at the beginning of the undrained shearing for all tested samples. Subsequent undrained behaviour in triaxial compression and extension is analyzed in detail. Previous deviatoric strain histories can progressively transform the compressive and unstable behaviour of loose sand into a dilative and stable behaviour of dense-like sand, while being loose. Experiments show a common response induced by recent strain histories in terms of effective stress paths, independently of the axial strain attained during the drained presheared cycle, a unique initial gradient of the effective stress paths, a progressive appearance of dilatancy, an evolution the undrained behaviour and a systematic partial static liquefaction associated with softer behaviour when sheared in the opposite direction of the initial presheared direction. This paper offers a comprehensive understanding of the mechanisms of a specialized induced anisotropy created by simple linear stress paths in the classical triaxial plane.

Cyclic and post-cyclic monotonic behavior of crushed conglomerate rockfill material under dry and saturated conditions

The seismic behavior of two conglomerate rockfill materials used in two high rockfill dams, subjected to earthquake loads, has been studied. In order to evaluate the dynamic behavior, an extensive series of monotonic and cyclic tests were carried out on large cylindrical specimens of conglomerate rockfill materials using triaxial tests. This paper first studies the effects of drainage (dry, saturation) conditions on the mechanical behavior of conglomerate rockfills at two compaction levels, and grain size distribution subjected to monotonic loading. Loading frequency and drainage condition effects on specimen behavior have been studied under cyclic loads under both isotropic and anisotropic initial stress conditions. To study any sign of material degradation due to cyclic loading, the post-cyclic monotonic stress–strain curves were compared under “dry” and “saturated” conditions. Geotechnical parameters to be used in static and dynamic numerical analyses models have also been presented.

Strength mobilization in clays and silts

A large database of 115 triaxial, direct simple shear, and cyclic tests on 19 clays and silts is presented and ana- lysed to develop an empirical framework for the prediction of the mobilization of the undrained shear strength, cu, of natural clays tested from an initially isotropic state of stress. The strain at half the peak undrained strength (gM=2) is used to normal- ize the shear strain data between mobilized strengths of 0.2cu and 0.8cu. A power law with an exponent of 0.6 is found to describe all the normalized data within a strain factor of 1.75 when a representative sample provides a value for gM=2. Multi-linear regression analysis shows that gM=2 is a function of cu, plasticity index Ip, and initial mean effective stress p 0 0. Of the 97 stress-strain curves for which cu, Ip, and p 0 were available, the observed values of gM=2 fell within a factor of three of the regression; this additional uncertainty should be acknowledged if a designer wished to limit immediate founda- tion settlements on the basis of an undrained strength profile and the plasticity index of the clay. The influence of stress his- tory is also discussed. The application of these stress-strain relations to serviceability design calculations is portrayed through a worked example. The implications for geotechnical decision-making and codes of practice are considered.