Plane Strain Apparatus Research Articles

Improvement and Validation of a Newly Developed Plane Strain Apparatus Based on True Triaxial Testing

Abstract The plane strain apparatus is an important instrument for studying the strength and deformation characteristics of soil with a specific stress path under plane strain condition and it is indispensable for theoretically studying rock and soil mechanics. After reviewing and summarizing the development history of the plane strain apparatus, we improved the pressure chamber, stress measuring mechanism, loading mechanism, and created a pressure chamber that can simulate a plane strain state. This improvement was based on the true triaxial apparatus with vertical rigidity and flexible loading in two orthogonal horizontal planes developed by the Xi’an University of Technology. We conducted plane strain tests of intact loess and remolded loess under different water contents and consolidation confining pressures. The rationality and reliability of the modification were verified by comparing the stress–strain curves and strength parameters obtained from plane strain and conventional triaxial tests, such that the evolution law of intermediate principal stress and the intermediate principal stress coefficient in the plane strain shear process was preliminarily revealed. Subsequently, the coefficient of intermediate principal stress at failure was found to be between 0.13 and 0.53. Thus, the effective modification of the plane strain apparatus can provide an experimental means for studying the strength and deformation characteristics of soil under plane strain condition.

Yielding and K 0 Value Variation of Cemented Sand along a K 0 Path

The yield stress and the coefficient of lateral earth pressure at rest, K0, of soil are important parameters for geotechnical design. However, the effect of cementation on the values of yield stress and K0 of artificially cemented sand along a K0 path has not been fully studied, despite the common use of cement mixing for soil improvement. A series of consolidation tests of K0 on artificially cemented sand has been conducted using a plane-strain apparatus. The test results show that the value of K0 of cemented sand is very much affected by the amount of cementation; the lowest value of K0 in a K0 test corresponds to the yield stress provided by cementation. It is established in this study that the yield stress of cemented sand marks the start of a large amount of bond destruction. The value of K0 reduces exponentially with the increase in cement content. One important practical implication is that the lateral earth pressure at rest can be reduced by introducing cementation to soil. This study also shows that Jaky’s equation is no longer applicable for estimating the value of K0 of cemented sand, although it may still provide a rough estimate for clean sand. The value of K0 of cemented sand can be estimated using a combination of Jaky’s equation for clean sand and Jaky’s equation for cement content.

A novel multiscale neutron-diffraction-based experimental approach for granular media

The complexity of granular (geo-)materials is associated with the mobility and interaction of their constituent particles. Under the effect of loading, these materials exhibit a highly inhomogeneous behaviour, which might vary significantly as the loading develops (i.e. certain grain assemblies take up the load whilst other, neighbouring assemblies fall into states of lower load). To that end, understanding the (micro-)mechanisms related to the distribution and evolution of forces/stresses through granular media requires appropriate, spatially resolved measurements. Neutron strain scanning (NSS) is an experimental technique based on diffraction measurements that has been successfully used in recent years to infer force/stress distribution in granular materials under load, by measuring the crystallographic strains of grains. In this work, first results from a new experimental approach involving simultaneous NSS and digital image correlation (DIC) of quartz sand under load in a specially designed plane-strain apparatus are presented. The combined use of these techniques allows the investigation of deformation mechanisms in granular media, such as sand, at different scales. Therefore, a completely novel multiscale analysis of granular (geo-)materials can be made – that is, associating the traditional macroscale measurements with the mesoscale characterisation of the strain field (through DIC) and the inferred microscale stress distribution (through NSS).

Theoretical and experimental bifurcation analysis of rock under plane strain compression

A new plane strain apparatus for rock testing was designed and built, and a series of plane strain tests on sandstone was performed. The formation and orientation of localization in sandstone were studied theoretically within the framework of equilibrium bifurcation theory. Corresponding elastoplastic constitutive models with nonlinear yield and potential functions were developed and fitted on the plane strain test data. The inclination of the shear band and the bifurcation point were predicted using the acoustic tensor method. The comparison of the computational and experimental results indicates that the initiation of a shear band predicted by a two-dimensional model could occur within the strain hardening region (i.e. prior to the peak stress), and the predicted orientations of the shear bands agreed qualitatively with those measured.

Strength Testing of Sandstone Under Multi-Axial Stress States

A true triaxial apparatus was designed and fabricated to achieve multi-axial stress states with prismatic specimens. The device, which is a modification of the University of Minnesota plane-strain apparatus, is equipped with piston assemblies that generate the intermediate principal stress. A closed-loop, servo-hydraulic load frame is used to control the major principal stress, while the minor principal stress is developed by fluid pressure. A stress path was developed to perform experiments under various states of stress at constant mean stress. Results from strength testing on Dunnville sandstone under conventional compression and extension are compared with the results performed under multi-axial stress states. Failure data were plotted in principal stress space to investigate the effect of intermediate stress on strength. A plane fitting method was used to obtain the material parameters of two, six-sided Paul–Mohr–Coulomb failure surfaces, which capture the strength characteristics of the sandstone over a range of mean stress.

A plane strain testing apparatus characterized by flexible loading and noncontact deformation measurement and its application to the study of shear band failure of sand

A new type of plane strain apparatus is developed to study the mechanical properties and shear band failure of soil, which possesses the advantages of flexible loading for lateral confining pressure and noncontact measurement and high measurement accuracy for surface deformation. In addition, the whole deformation procedure of the specimen can be recorded with images, which can be used to describe the development of strain localization and the shear band. It can be seen that the deformation process has three obvious stages, that is, the hardening stage, the softening stage, and the residual stage. The measured inclination angles of shear bands decrease as confining pressure or the mean size increases. In addition, it can be observed that the sand presents continuing growth of the unrecoverable plastic deformation inside the shear band and exhibits almost elastic deformation outside. From the detection results for local points in the specimen, the stress–strain relationships are different for different parts, and the sand sample behaves like an uneven structure instead of an even element, which means that the usual method of measuring the stress–strain relationship of the soil sample is only a macroscopic approximation.

Optical quantification of suffosion in plane strain physical models

Suffosion is a seepage-induced instability phenomenon whereby fines are eroded away through the constrictions formed by coarse particles, resulting in a reduction in soil volume and a change in hydraulic conductivity. In this study, upward seepage tests were performed on gap-graded soil containing coloured fines in a plane strain apparatus. A series of images was recorded through a transparent window to quantify the features of suffosion. The estimated cumulative eroded soil mass from image analysis was found to generally agree with independent macroscopic observations, indicating that optical analysis allows an easy identification of suffosion characteristics. For the tested soil, the fines were prone to be transported within an instant period of increasing hydraulic gradient, with few of them moving during the constant flow. Furthermore, the volume of the specimen was reduced due to suffosion, leading to an alternation of preferred coarse particle orientations in the observation field.

Plane Strain Testing with Passive Restraint

A plane strain condition for testing rock is developed through passive restraint in the form of a thick- walled cylinder. The so-called biaxial frame generates the intermediate principal stress that imposes a triaxial state of stress on a prismatic specimen. Major and minor principal stresses and corresponding strains are accurately measured, providing data to calculate the elastic (Young's modulus and Poisson's ratio), inelastic (dilatancy angle), and strength (friction angle and cohesion) parameters of the rock. Results of experiments conducted on Indiana lime- stone in plane strain compression are compared with the results of axisymmetric compression and extension. With proper system calibration, Young's modulus and Poisson's ratio are consistent among the tests. The plane strain apparatus enforces in-plane deformation with the three principal stresses at failure being different, and it allows one to determine the Paul-Mohr-Coulomb failure surface, which includes an intermediate stress effect.

Factors affecting pre-failure instability of sand under plane-strain conditions

Experimental data obtained from a plane-strain apparatus are presented in this paper to show that a pre-failure instability in the form of a rapid and sustained increase in strain rate can occur for both contractive and dilative sand under fully drained conditions. However, this type of instability is different from the runaway type of instability observed under undrained conditions, and has therefore been called conditional instability. Despite the differences, the conditions for both types of instability are the same for contractive sand. There are also other factors that affect the pre-failure instability of sand observed in the laboratory. These include the stress ratio, void ratio, sand state, load control mode and reduction rate of the effective confining stress. In this paper, these factors are discussed and analysed using experimental data obtained from undrained instability (or creep) tests and constant shear drained (CSD) tests carried out under plane-strain conditions.

Pre-Failure Instability Behavior of Sand in Strain Path Testing Under Plane-Strain Conditions

ABSTRACT Experimental data are presented in this paper to study the instability behavior of sand in strain path testing under plane-strain conditions. K0 consolidated strain path tests were conducted on Changi sand using a plane-strain apparatus. The test results show that the occurrence of pre-failure instability under plane-strain conditions is affected by the void ratio and the strain increment ratio. This is consistent with previous findings established under axisymmetric conditions. However, instability behavior of medium dense sand in strain path-controlled plane-strain tests can also be affected by shear band formation. In this case, on-failure instability takes place and failure is likely caused by shear band development. This observation is different from that in triaxial strain path-controlled tests where shear bands do not normally occur.

Compressibility of Changi sand in K0consolidation

The one-dimensional compressibility of sand is an important property for the estimation of settlement or deformation of sand deposits. The <TEX>$K_0$</TEX> value of sand is also an important design parameter. Experimental results are presented in this paper to study the compressibility of sand in <TEX>$K_0$</TEX> consolidation tests. The <TEX>$K_0$</TEX> consolidation tests were carried out using a triaxial cell and a plane-strain apparatus. Specimens prepared using both the moist tamping and the water sedimentation methods were tested. The testing data demonstrate that the type of testing apparatus does not affect the <TEX>$K_0$</TEX> measurement if proper boundary conditions are imposed in the tests. The data also show that the compressibility and the <TEX>$K_0$</TEX> value of loose sand specimens prepared using the moist tamping method are very sensitive to the variation of void ratio. The <TEX>$K_0$</TEX> values measured from these tests do not agree with the <TEX>$K_0$</TEX> values calculated from Jaky's equation. The compressibility and <TEX>$K_0$</TEX> values of sand obtained from tests on specimens prepared using different preparation methods are different which may reflect the influence of soil fabrics or structures on the one dimensional compression behavior of sand.

Effect of Loading Mode on Strain Softening and Instability Behavior of Sand in Plane-Strain Tests

Experimental data to study the effect of loading mode on the strain softening and instability behavior of sand under plane-strain conditions are presented in this paper. A new plane-strain apparatus was adopted to conduct K0 consolidated drained and undrained tests under both deformation-controlled and load-controlled loading modes. The drained behavior of very loose and medium dense sand and the undrained behavior of very loose sand under plane-strain conditions were characterized. The test results show that the loading mode affects the postpeak behavior and controls whether strain softening or instability will occur in the postpeak region. Shear bands occurred in tests conducted on medium dense sand, but not in tests for very loose sand. The failure line and critical state line are not affected by the loading mode. The study also shows that the concept of a unique “ultimate state” for both dense and loose sand as previously established based on conventional drained triaxial tests is not supported by the...

Shear Strength of Jumunjin Sand according to Relative Density

The properties of sands pertaining to shear strength have been studied extensively by plane strain and triaxial tests for relative densities above 40%. Unfortunately, properties of sand have not been comprehensively studied for relative density below 40%. An experimental investigation of the shear strength of Jumunjin sand was carried out using a plane strain, triaxial and direct shear apparatus according to relative density ranges from 0 to 100%. Because of the complexity of the shear tests on coarse materials, correlations were developed that would be useful for practical purposes. This article presents a comparison of strength properties' results and their correlation with relative density.

Strain-softening behaviour of sand in strain path testing under plane-strain conditions

Experimental data are presented in this paper to study the strain-softening behaviour of sand under plane-strain conditions. K0 consolidated strain path tests were conducted using a new plane-strain apparatus. The stress–strain behaviour of medium dense sand under plane-strain conditions was characterized. The test results show that the occurrence of pre-failure strain softening under plane-strain conditions is affected by the void ratio, the strain increment ratio and the initial effective confining stress. This is consistent with previous findings established under axisymmetric conditions. However, a pre-failure strain-softening behaviour in plane-strain tests conducted under high-confining stresses may consist of three stages, namely, material softening, banding softening, and ultimate state. This observation is different from that in triaxial tests where banding softening does not normally occur.

Influence of Membrane and Filter Paper on Plane-Strain Testing of Soft Sedimentary Rock

Abstract It is recognized that the intermediate principal stress plays an important role in the strength and the stress-dilatancy relation of soft sedimentary rock. However, few plane-strain/true triaxial experiments on soft rock have been referenced in literature due to the relatively high strength of geomaterials. With a conventional plane-strain apparatus, equipped with a prefixed plane-strain confining frame, it is difficult to obtain real isotropic consolidation before shearing. On the other hand, it has been found that the influence of the membrane/covering material on a high-strength specimen cannot be ignored. In this study, therefore, an innovative plane-strain test system for soft rock, that can overcome the shortcomings of the conventional type of apparatus, and issues related to specimen preparation are introduced. The results of drained compression tests and drained creep tests, along with theoretical simulations, are reported. The influence of the membrane and the filter paper are illustrated by a simple finite element method. A combination of experimental and theoretical approaches is employed to facilitate the understanding of the mechanical behavior of soft rock.

K0of sand measured by a plane-strain apparatus

Experimental results are presented in this note to study the coefficient of lateral earth pressure at rest, K0, of sand measured using a plane-strain apparatus. The data are also compared with the K0measured by triaxial K0consolidation tests. The test data show that the K0values measured for specimens prepared using the water sedimentation method vary little with the void ratio of the soil, and therefore do not agree with the K0values calculated using Jaky’s equation, which uses the peak friction angles obtained from either plane-strain or triaxial tests. The K0values measured for specimens prepared using the moist tamping method follow a linear relationship with the void ratio. However, this relationship does not agree with Jaky’s equation either. The K0values obtained from tests on the specimens prepared using the two different preparation methods are different, which may reflect the influence of soil fabrics or structures on the one-dimensional compression behaviour of soil.

Strain softening of K0-consolidated Changi sand under plane-strain conditions

Experimental results are presented in this pa- per to study the strain softening behaviour of a marine dredged sand under plane-strain conditions. K0 consoli- dated drained and undrained tests were conducted using a new plane-strain apparatus to characterize the strain softening behaviour of the sand under plane-strain con- ditions. For medium dense specimens, strain softening and shear bands were observed to occur under both drained and undrained conditions. For very loose specimens, no shear bands were observed and critical states were reached within the homogeneous deformation region in both drained and undrained tests. Strain softening was observed to occur at small strain for very loose specimens under undrained conditions. Two types of strain softening, the homogenous softening and banding softening, were identified and the conditions for strain softening were established. The results obtained from this study were compared with the studies by Han and Vardoulakis (Geotechnique 41(1):49-78, 1991), Finno et al. (J Geotech Eng ASCE 122(6):462-473, 1996, Geotechnique 47(1):149-165, 1997) and Mokni and Desrues (Mech Cohes-Frict Mat 4:419-441, 1998).

Stress-Strain Behavior of a Granular Fill Measured by a New Plane-Strain Apparatus

Abstract In this paper a new plane-strain apparatus is described. The main feature of the plane-strain apparatus is that the intermediate principal stress can be measured by four submersible pressure transducers. Experimental data obtained from drained tests on very loose to medium dense sand are presented. The strength and deformation behavior of the sand under plane-strain conditions and shear band formation are studied. The results show that the failure envelope obtained from plane-strain tests is lower than that from triaxial tests. However, in terms of friction angle, the value obtained from plane-strain tests is higher than that from triaxial tests. The critical state line obtained under plane-strain conditions is also different from that under axisymmetric conditions. Under plane-strain conditions, shear bands occur for medium loose to dense specimens. However, no visible shear bands are observed for very loose specimens. This is consistent with the study reported by Han and Vardoulakis (1991) but different from that by Finno et al. (1996, 1997).

The Louisiana Plane Strain Apparatus for Soil Testing

Abstract The mechanical description of a new plane strain (biaxial) apparatus for soil testing is presented. The design took into consideration flexibility in accomodating different specimen sizes, easy assembly procedure, and well-controlled boundary conditions. The apparatus is well instrumented with load, displacement, and pressure sensors and has the capabilities to capture localization and shear band development. A comparison between two experiments that were conducted on F-75 Ottawa sand is presented and the effect of inhibiting lateral movement of bottom end platen is presented and discussed. It has been found that restraining lateral movement of bottom end platen has resulted in higher peak and residual load values.

Determination of plane-strain shear strength of sand from the results of triaxial tests

Experimental investigation of the shear strength of dry sands was carried out using triaxial and plane-strain apparatus. The results were used to evaluate Rowe's stress–dilatancy theory, the relationships between the shear strength components due to friction and interlocking, and the volume-change characteristics for cases of plane-strain and axisymmetric boundary conditions. Because of the complexity of the plane-strain testing apparatus in the normal soil mechanics laboratory and the difficulties involved in performing this type of shear test, it is becoming costly to obtain plane-strain test results for consulting purposes. Based on Rowe's stress–dilatancy theory, the results of the present investigation, and the available test results in the literature, two simple methods are proposed to predict the angle of shearing resistance for plane-strain conditions from the results of the conventional triaxial compression tests.Key words: shear strength, plane-strain test, triaxial test, sand, experimental investigation, geotechnical engineering.